Satyendra Nath Bose

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Satyendra Nath Bose

FRS, MP, PV
SatyenBose1925.jpg
Satyendra Nath Bose in 1925
Born(1894-01-01)1 January 1894
Calcutta, Bengal Presidency, British India
Died4 February 1974(1974-02-04) (aged 80)
Calcutta, India [1]
Nationality Indian
Alma mater University of Calcutta
Known for Bose–Einstein condensate
Bose–Einstein statistics
Bose–Einstein distribution
Bose–Einstein correlations
Bose gas
Boson
Ideal Bose Equation of State
Photon gas
Spouse(s)Ushabati Bose (née Ghosh [2] )
Awards Padma Vibhushan
Fellow of the Royal Society [3]
Scientific career
Fields Physics
Institutions University of Calcutta
University of Dhaka
Visva-Bharati
Academic advisors Jagadish Chandra Bose
Prafulla Chandra Ray
Doctoral students Purnima Sinha
Partha Ghose
Siva Brata Bhattacherjee
Other notable students Mani Lal Bhaumik
Lilabati Bhattacharjee
Asima Chatterjee
Ratan Lal Brahmachary
Member of Parliament, Rajya Sabha
In office
3 April 1952 2 April 1960
Signature
Signature Satyendranath Bose.svg

Satyendra Nath Bose FRS [3] (IPA:  [ʃotːendronatʰ boʃu] ; 1 January 1894 – 4 February 1974) was an Indian mathematician and physicist specialising in theoretical physics. He is best known for his work on quantum mechanics in the early 1920s, collaborating with Albert Einstein in developing the foundation for Bose–Einstein statistics and the theory of the Bose–Einstein condensate. A Fellow of the Royal Society, he was awarded India's second highest civilian award, the Padma Vibhushan in 1954 by the Government of India. [4] [5] [6]

Contents

The class of particles that obey Bose–Einstein statistics, bosons, was named after Bose by Paul Dirac. [7] [8]

A polymath, he had a wide range of interests in varied fields including physics, mathematics, chemistry, biology, mineralogy, philosophy, arts, literature, and music. He served on many research and development committees in sovereign India. [9]

Early life

Bose was born in Calcutta (now Kolkata), the eldest of seven children in a Bengali Kayastha [10] family. He was the only son, with six sisters after him. His ancestral home was in the village Bara Jagulia, in the then district of Nadia, in the Bengal Presidency. His schooling began at the age of five, near his home. When his family moved to Goabagan, he was admitted into the New Indian School. In the final year of school, he was admitted into the Hindu School. He passed his entrance examination (matriculation) in 1909 and stood fifth in the order of merit. He next joined the intermediate science course at the Presidency College, Calcutta, where his teachers included Jagadish Chandra Bose, Sarada Prasanna Das, and Prafulla Chandra Ray.

Bose received a Bachelor of Science in mixed mathematics from Presidency College, standing first in 1913. Then he joined Sir Ashutosh Mukherjee's newly formed Science College where he again stood first in the MSc mixed mathematics exam in 1915. His marks in the MSc examination created a new record in the annals of the University of Calcutta, which is yet to be surpassed. [11]

After completing his MSc, Bose joined the Science college, Calcutta University as a research scholar in 1916 and started his studies in the theory of relativity. It was an exciting era in the history of scientific progress. Quantum theory had just appeared on the horizon and important results had started pouring in. [11]

His father, Surendranath Bose, worked in the Engineering Department of the East Indian Railway Company. In 1914, at age 20, Satyendra Nath Bose married Ushabati Ghosh, [2] [12] the 11-year-old daughter of a prominent Calcutta physician. [13] They had nine children, two of whom died in early childhood. When he died in 1974, he left behind his wife, two sons, and five daughters. [11]

As a polyglot, Bose was well versed in several languages such as Bengali, English, French, German and Sanskrit as well as the poetry of Lord Tennyson, Rabindranath Tagore and Kalidasa. He could play the esraj , an Indian musical instrument similar to a violin. [14] He was actively involved in running night schools that came to be known as the Working Men's Institute. [6] [15]

Research career

Bose attended Hindu School in Calcutta, and later attended Presidency College, also in Calcutta, earning the highest marks at each institution, while fellow student and future astrophysicist Meghnad Saha came second. [6] He came in contact with teachers such as Jagadish Chandra Bose, Prafulla Chandra Ray and Naman Sharma who provided inspiration to aim high in life. From 1916 to 1921, he was a lecturer in the physics department of the Rajabazar Science College under University of Calcutta. Along with Saha, Bose prepared the first book in English based on German and French translations of original papers on Einstein's special and general relativity in 1919. In 1921, he joined as Reader of the Department of Physics of the recently founded University of Dhaka (in present-day Bangladesh). [16] Bose set up whole new departments, including laboratories, to teach advanced courses for MSc and BSc honours and taught thermodynamics as well as James Clerk Maxwell's theory of electromagnetism. [17]

Satyendra Nath Bose, along with Saha, presented several papers in theoretical physics and pure mathematics from 1918 onwards. In 1924, while working as a Reader (Professor without a chair) at the Physics Department of the University of Dhaka, Bose wrote a paper deriving Planck's quantum radiation law without any reference to classical physics by using a novel way of counting states with identical particles. This paper was seminal in creating the very important field of quantum statistics. [18] Though not accepted at once for publication, he sent the article directly to Albert Einstein in Germany. Einstein, recognising the importance of the paper, translated it into German himself and submitted it on Bose's behalf to the prestigious Zeitschrift für Physik . As a result of this recognition, Bose was able to work for two years in European X-ray and crystallography laboratories, during which he worked with Louis de Broglie, Marie Curie, and Einstein. [6] [19] [20] [21]

Bose–Einstein statistics

While presenting a lecture [22] at the University of Dhaka on the theory of radiation and the ultraviolet catastrophe, Bose intended to show his students that the contemporary theory was inadequate, because it predicted results not in accordance with experimental results.

In the process of describing this discrepancy, Bose for the first time took the position that the Maxwell–Boltzmann distribution would not be true for microscopic particles, where fluctuations due to Heisenberg's uncertainty principle will be significant. Thus he stressed the probability of finding particles in the phase space, each state having volume h3, and discarding the distinct position and momentum of the particles.

Bose adapted this lecture into a short article called "Planck's Law and the Hypothesis of Light Quanta" and sent it to Albert Einstein with the following letter: [23]

Respected Sir, I have ventured to send you the accompanying article for your perusal and opinion. I am anxious to know what you think of it. You will see that I have tried to deduce the coefficient 8π ν2/c3 in Planck's Law independent of classical electrodynamics, only assuming that the ultimate elementary region in the phase-space has the content h3. I do not know sufficient German to translate the paper. If you think the paper worth publication I shall be grateful if you arrange for its publication in Zeitschrift für Physik. Though a complete stranger to you, I do not feel any hesitation in making such a request. Because we are all your pupils though profiting only by your teachings through your writings. I do not know whether you still remember that somebody from Calcutta asked your permission to translate your papers on Relativity in English. You acceded to the request. The book has since been published. I was the one who translated your paper on Generalised Relativity.

Einstein agreed with him, translated Bose's papers "Planck's Law and Hypothesis of Light Quanta" into German, and had it published in Zeitschrift für Physik under Bose's name, in 1924. [24]

Possible outcomes of flipping two coins
Two headsTwo tailsOne of each
(1) There are three outcomes. What is the probability of producing two heads?
Outcome probabilities
 Coin 1
HeadTail
Coin 2HeadHHHT
TailTHTT
(2) Since the coins are distinct, there are two outcomes which produce a head and a tail. The probability of two heads is one-quarter.

The reason Bose's interpretation produced accurate results was that since photons are indistinguishable from each other, one cannot treat any two photons having equal energy as being two distinct identifiable photons. By analogy if, in an alternate universe, coins were to behave like photons and other bosons, the probability of producing two heads would indeed be one-third (tail-head = head-tail).

Bose's interpretation is now called Bose–Einstein statistics. This result derived by Bose laid the foundation of quantum statistics, and especially the revolutionary new philosophical conception of the indistinguishability of particles, as acknowledged by Einstein and Dirac. [24] When Einstein met Bose face-to-face, he asked him whether he had been aware that he had invented a new type of statistics, and he very candidly said that no, he wasn't that familiar with Boltzmann's statistics and didn't realize that he was doing the calculations differently. He was equally candid with anyone who asked.

Bose–Einstein condensate

Velocity-distribution data of a gas of rubidium atoms, confirming the discovery of a new phase of matter, the Bose-Einstein condensate. Left: just before the appearance of a Bose-Einstein condensate. Center: just after the appearance of the condensate. Right: after further evaporation, leaving a sample of nearly pure condensate. Bose Einstein condensate.png
Velocity-distribution data of a gas of rubidium atoms, confirming the discovery of a new phase of matter, the Bose–Einstein condensate. Left: just before the appearance of a Bose–Einstein condensate. Center: just after the appearance of the condensate. Right: after further evaporation, leaving a sample of nearly pure condensate.

Einstein also did not at first realize how radical Bose's departure was, and in his first paper after Bose, he was guided, like Bose, by the fact that the new method gave the right answer. But after Einstein's second paper using Bose's method in which Einstein predicted the Bose-Einstein condensate (pictured left), he started to realize just how radical it was, and he compared it to wave/particle duality, saying that some particles didn't behave exactly like particles. Bose had already submitted his article to the British Journal Philosophical Magazine, which rejected it before he sent it to Einstein. It is not known why it was rejected. [26]

Einstein adopted the idea and extended it to atoms. This led to the prediction of the existence of phenomena which became known as Bose–Einstein condensate, a dense collection of bosons (which are particles with integer spin, named after Bose), which was demonstrated to exist by experiment in 1995.

Dhaka

Bose at Dhaka University in the 1930s Satyendra-nath-bose.jpg
Bose at Dhaka University in the 1930s

After his stay in Europe, Bose returned to Dhaka in 1926. He did not have a doctorate, and so ordinarily, under the prevailing regulations, he would not be qualified for the post of Professor he applied for, but Einstein recommended him. He was then made Head of the Department of Physics at Dhaka University. He continued guiding and teaching at Dhaka University.

Bose designed equipment himself for an X-ray crystallography laboratory. He set up laboratories and libraries to make the department a center of research in X-ray spectroscopy, X-ray diffraction, magnetic properties of matter, optical spectroscopy, wireless, and unified field theories. He also published an equation of state for real gases with Meghnad Saha. He was also the Dean of the Faculty of Science at Dhaka University until 1945.

Calcutta

When the partition of India became imminent (1947), he returned to Calcutta (now known as Kolkata) and taught there until 1956. He insisted every student design his own equipment using local materials and local technicians. He was made professor emeritus on his retirement. [19] [27] [6] He then became Vice-Chancellor of Visva-Bharati University in Santiniketan. He returned to the University of Calcutta to continue research in nuclear physics and complete earlier works in organic chemistry. In subsequent years, he worked in applied research such as extraction of helium in hot springs of Bakreshwar. [28]

Other fields

Apart from physics, he did some research in biotechnology and literature (Bengali and English). He made deep studies in chemistry, geology, zoology, anthropology, engineering and other sciences. Being Bengali, he devoted a lot of time to promoting Bengali as a teaching language, translating scientific papers into it, and promoting the development of the region. [20] [29] [5]

Honours

S N Bose with other scientists at Calcutta University M N Saha, J C Bose, J C Ghosh, Snehamoy Dutt, S N Bose, D M Bose, N R Sen, J N Mukherjee, N C Nag.jpg
S N Bose with other scientists at Calcutta University
Bust of Satyendra Nath Bose which is placed in the garden of Birla Industrial & Technological Museum. Bust of Satyendra Nath Bose at BITM 13 July 14 006.jpg
Bust of Satyendra Nath Bose which is placed in the garden of Birla Industrial & Technological Museum.

In 1937, Rabindranath Tagore dedicated his only book on science, Visva–Parichay, to Satyendra Nath Bose. Bose was honoured with title Padma Vibhushan by the Indian Government in 1954. In 1959, he was appointed as the National Professor, the highest honour in the country for a scholar, a position he held for 15 years. In 1986, the S.N. Bose National Centre for Basic Sciences was established by an act of Parliament, Government of India, in Salt Lake, Calcutta. [30] [31]

Bose became an adviser to the then newly formed Council of Scientific and Industrial Research. He was the President of Indian Physical Society and the National Institute of Science. He was elected General President of the Indian Science Congress. He was the Vice-President and then the President of Indian Statistical Institute. In 1958, he became a Fellow of the Royal Society. He was nominated as member of Rajya Sabha.

Partha Ghose has stated that [6]

Bose's work stood at the transition between the 'old quantum theory' of Planck, Bohr and Einstein and the new quantum mechanics of Schrodinger, Heisenberg, Born, Dirac and others.

Nobel Prize nomination

S.N. Bose was nominated by K. Banerji (1956), D.S. Kothari (1959), S.N. Bagchi (1962), and A.K. Dutta (1962) for the Nobel Prize in Physics, for his contribution to Bose-Einstein statistics and the unified field theory. For instance, Kedareswar Banerjee, head of the Physics Department, University of Allahabad, in a letter of 12 January 1956 wrote to the Nobel Committee as follows: “(1). He (Bose) made very outstanding contributions to Physics by developing the statistics known after his name as Bose statistics. In recent years this statistics is found to be of profound importance in the classifications of fundamental particles and has contributed immensely to the development of nuclear physics. (2). During the period from 1953 to date, he has made a number of highly interesting contributions of far-reaching consequences on the subject of Einstein’s Unitary Field Theory.” Bose's work was evaluated by an expert of the Nobel Committee, Oskar Klein, who did not see his work worthy of a Nobel Prize. [32] [33] [34]

Legacy

Bose on a 1994 stamp of India Satyendranath Bose 1994 stamp of India.jpg
Bose on a 1994 stamp of India

Bosons, a class of elementary subatomic particles in particle physics were named after Satyendra Nath Bose to commemorate his contributions to science. [35] [36]

Although seven Nobel Prizes were awarded for research related to S N Bose's concepts of the boson, Bose–Einstein statistics and Bose–Einstein condensate, Bose himself was not awarded a Nobel Prize.

In his book The Scientific Edge, physicist Jayant Narlikar observed:

SN Bose's work on particle statistics (c. 1922), which clarified the behaviour of photons (the particles of light in an enclosure) and opened the door to new ideas on statistics of Microsystems that obey the rules of quantum theory, was one of the top ten achievements of 20th century Indian science and could be considered in the Nobel Prize class. [37]

When Bose himself was once asked that question, he simply replied, "I have got all the recognition I deserve"— probably because in the realms of science to which he belonged, what is important is not a Nobel, but whether one's name will live on in scientific discussions in the decades to come. [38]

Works (selection)

Related Research Articles

Absolute zero The lowest attainable temperature

Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvins. The fundamental particles of nature have minimum vibrational motion, retaining only quantum mechanical, zero-point energy-induced particle motion. The theoretical temperature is determined by extrapolating the ideal gas law; by international agreement, absolute zero is taken as −273.15° on the Celsius scale, which equals −459.67° on the Fahrenheit scale. The corresponding Kelvin and Rankine temperature scales set their zero points at absolute zero by definition.

Bose–Einstein condensate State of matter

In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter which is typically formed when a gas of bosons at low densities is cooled to temperatures very close to absolute zero. Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point microscopic quantum mechanical phenomena, particularly wavefunction interference, become apparent macroscopically. A BEC is formed by cooling a gas of extremely low density to ultra-low temperatures.

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In particle physics, a fermion is a particle that follows Fermi–Dirac statistics and generally has half odd integer spin: spin 1/2, spin 3/2, etc. These particles obey the Pauli exclusion principle. Fermions include all quarks and leptons, as well as all composite particles made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons, which obey Bose–Einstein statistics.

Photon Elementary particle or quantum of light

The photon is a type of elementary particle. It is the quantum of the electromagnetic field including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always move at the speed of light in vacuum, 299792458 m/s. The photon belongs to the class of bosons.

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Bose–Einstein statistics Statistical description for the behavior of bosons

In quantum statistics, Bose–Einstein (B–E) statistics describe one of two possible ways in which a collection of non-interacting, indistinguishable particles may occupy a set of available discrete energy states at thermodynamic equilibrium. The aggregation of particles in the same state, which is a characteristic of particles obeying Bose–Einstein statistics, accounts for the cohesive streaming of laser light and the frictionless creeping of superfluid helium. The theory of this behaviour was developed (1924–25) by Satyendra Nath Bose, who recognized that a collection of identical and indistinguishable particles can be distributed in this way. The idea was later adopted and extended by Albert Einstein in collaboration with Bose.

Quantum optics is a branch of atomic, molecular, and optical physics dealing with how individual quanta of light, known as photons, interact with atoms and molecules. It includes the study of the particle-like properties of photons. Photons have been used to test many of the counter-intuitive predictions of quantum mechanics, such as entanglement and teleportation, and are a useful resource for quantum information processing.

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Bose gas State of matter of many bosons

An ideal Bose gas is a quantum-mechanical phase of matter, analogous to a classical ideal gas. It is composed of bosons, which have an integer value of spin, and obey Bose–Einstein statistics. The statistical mechanics of bosons were developed by Satyendra Nath Bose for a photon gas, and extended to massive particles by Albert Einstein who realized that an ideal gas of bosons would form a condensate at a low enough temperature, unlike a classical ideal gas. This condensate is known as a Bose–Einstein condensate.

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In quantum mechanics, a boson is a particle that follows Bose–Einstein statistics. Bosons make up one of two classes of elementary particles, the other being fermions. The name boson was coined by Paul Dirac to commemorate the contribution of Satyendra Nath Bose, an Indian physicist and professor of physics at University of Calcutta and at University of Dhaka in developing, with Albert Einstein, Bose–Einstein statistics, which theorizes the characteristics of elementary particles.

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Debendra Mohan Bose Indian physicist (1885–1975)

Debendra Mohan Bose was an Indian physicist who made contributions in the field of cosmic rays, artificial radioactivity and neutron physics. He was the longest serving Director (1938–1967) of Bose Institute. Bose was the nephew of the famous physicist Jagadish Chandra Bose, who laid the foundations of modern science in India.

Kameshwar C. Wali

Kameshwar C. Wali is the Distinguished Research Professor of Physics Emeritus at Syracuse University's College of Arts and Sciences. He is a specialist in high energy physics, particularly symmetries and dynamics of elementary particles, and as the author of Chandra: A Biography of S. Chandrasekhar and Cremona Violins: a physicist's quest for the secrets of Stradivari.

In Bangladesh, the cultivation of modern science started during the British rule when the first modern educational institutions, focused on scientific fields, were established in the country. The University of Dhaka, established in 1921, acted as the driving force in producing many renowned scientists in Bangladesh.

Bangiya Bijnan Parishad An organization to promote science

Bangiya Bijnan Parishad is a science organization founded by Satyendra Nath Bose in 1948. As a science organization, the Bangiya Bijnan Parishad led the Science-Movement. Nowadays, many science movement organization take the inspiration from Bangiya Bijnan Parishad directly or indirectly.

Rajabazar Science College Science College, Kolkata, West Bengal

The Rashbehari Siksha Prangan is a university campus, one of five main campuses of University of Calcutta (CU). The college served as the cradle of Indian Sciences by winning the Nobel Prize in Physics in 1930 and many fellowships of the Royal Society London.

References

  1. "Satyendra Nath Bose – Bengali physicist". Encyclopædia Britannica . Retrieved 5 December 2015.
  2. 1 2 "S.N. Bose Biography Project". July 2012.
  3. 1 2 Mehra, J. (1975). "Satyendra Nath Bose 1 January 1894 – 4 February 1974". Biographical Memoirs of Fellows of the Royal Society . 21: 116–126. doi:10.1098/rsbm.1975.0002. S2CID   72507392.
  4. Wali 2009, pp. xv, xxxiv.
  5. 1 2 Barran, Michel, "Bose, Satyendranath (1894–1974)", Science world (biography), Wolfram.
  6. 1 2 3 4 5 6 Mahanti, Dr Subodh. "Satyendra Nath Bose, The Creator of Quantum Statistics". IN: Vigyan Prasar.
  7. Farmelo, Graham, "The Strangest Man", Notes on Dirac's lecture Developments in Atomic Theory at Le Palais de la Découverte, 6 December 1945, UKNATARCHI Dirac Papers, p. 331, note 64, BW83/2/257889.
  8. Miller, Sean (18 March 2013). Strung Together: The Cultural Currency of String Theory as a Scientific Imaginary. University of Michigan Press. p. 63. ISBN   978-0-472-11866-3.
  9. Wali 2009, p. xl.
  10. Santimay Chatterjee; Enakshi Chatterjee (1976). Satyendra Nath Bose. National Book Trust, India. p. 12. Satyendra Nath was born in Calcutta on the first of January, 1894, in a high caste Kayastha family with two generations of English education behind him.
  11. 1 2 3 Kamble, Dr VB (January 2002). "Vigyan Prasar".
  12. Wali 2009, p. xvii.
  13. Masters, Barry R. (April 2013). "Satyendra Nath Bose and Bose-Einstein Statistics" (PDF). Optics & Photonics News. 24 (4): 41. Bibcode:2013OptPN..24...40M. doi:10.1364/OPN.24.4.000040.
  14. "Vigyan Prasar – SC Bose". www.vigyanprasar.gov.in. Government of India. Retrieved 14 June 2017.
  15. Wali 2009, p. xvi.
  16. Md Mahbub Murshed (2012), "Bose, Satyendra Nath", in Sirajul Islam and Ahmed A. Jamal (ed.), Banglapedia: National Encyclopedia of Bangladesh (Second ed.), Asiatic Society of Bangladesh
  17. Wali 2009, pp. xvii, xviii, xx.
  18. Bose, S. N. (1994). "Planck's Law and the Light Quantum Hypothesis" (PDF). Journal of Astrophysics and Astronomy. 15: 3–7. Bibcode:1994JApA...15....3B. doi:10.1007/BF03010400. S2CID   121808581.
  19. 1 2 Shanbhag, MR. "Scientist". Personalities. Calcutta web. Archived from the original on 2 August 2002.
  20. 1 2 O'Connor, JJ; Robertson, EF (October 2003). "Satyendranath Bose". The MacTutor History of Mathematics archive. UK: St Andrew's.
  21. Wali 2009, pp. xx–xxiii.
  22. Shanbhag, MR. "Satyendra Nath Bose (January 1, 1894 – February 4, 1974)". Indian Statistical Institute.
  23. Venkataraman, G (1992), Bose And His Statistics, Universities Press, p. 14, ISBN   978-81-7371-036-0
  24. 1 2 Wali 2009, p. 414.
  25. "Quantum Physics; Bose Einstein condensate", Image Gallery, NIST, 11 March 2006.
  26. A.Douglas Stone, Chapter 24, The Indian Comet, in the book Einstein and the Quantum, Princeton University Press, Princeton, New Jersey, 2013.
  27. Wali 2009, pp. xxx, xxiv.
  28. Wali 2009, pp. xxxvi, xxxviii.
  29. Wali 2009, pp. xxiv, xxxix.
  30. Wali 2009, pp. xxxiv, xxxviii.
  31. Ghose, Partha (3 January 2012), "Original vision", The Telegraph (Opinion), IN .
  32. Singh, Rajinder (2016) India's Nobel Prize Nominators and Nominees – The Praxis of Nomination and Geographical Distribution, Shaker Publisher, Aachen, pp. 26–27. ISBN   978-3-8440-4315-0
  33. Singh, Rajinder (2016) Die Nobelpreise und die indische Elite, Shaker Verlag, Aachen, pp. 24–25. ISBN   978-3-8440-4429-4
  34. Singh, Rajinder (2016) Chemistry and Physics Nobel Prizes – India's Contribution, Shaker Verlag, Aachen. ISBN   978-3-8440-4669-4
  35. Daigle, Katy (10 July 2012). "India: Enough about Higgs, let's discuss the boson". AP News . Retrieved 10 July 2012.
  36. Bal, Hartosh Singh (19 September 2012). "The Bose in the Boson". New York Times blog. Retrieved 21 September 2012.
  37. Narlikar, Jayant V (2003), The Scientific Edge: The Indian Scientist from Vedic to Modern Times, Penguin Books, p. 127, ISBN   978-0-14-303028-7 . The work of other 20th century Indian scientists which Narlikar considered to be of Nobel Prize class were Srinivasa Ramanujan, Chandrasekhara Venkata Raman and Megh Nad Saha.
  38. Alikhan, Anvar (16 July 2012). "The Spark in a Crowded Field". Outlook India. Retrieved 10 July 2012.
Academic offices
Preceded by
Indira Devi Chaudhurani
Upacharya, Vishwa Bharati
1956–58
Succeeded by
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