Indranil1993

This is the User Page of Indranil(English: /ˈɪnðroʊniːl/) Roy.

About me

I am a research scholar of Tata Institute of Fundamental Research, Mumbai in the Department of Condensed Matter Physics and Material Sciences ^[1].

I want to edit the Wikipedia page on Fock state.

In the wikipedia page, I want to start from editing the definition of Fock state ^[2]. I want to add that, Fock states are those kets of Fock space, which are eigenkets of number operator. And mathematical formalism of constructing Fock state by denoting occupation number of a state, and hence action of number operator on a general Fock state can be shown. And this can work as the formal definition of a Fock state.

In the next part, under heading 'Example using 2 particles': I can show that even if the Fock state of 2 particles is symmetric or antisymmetric under exchange of kets of individual particles, action by a number operator gives the same result.

In the next part, under heading 'Bosonic Fock state': by calling the fock states, corresponding to symmetric behaviour of the state due to action of exchange operator, as bosonic fock states; action of creation and annihilation operators on that state can be shown. And hence action of number operator can be shown.

In the next part, under heading 'Fermionic Fock state': by calling the fock states, corresponding to antisymmetric behaviour of the state due to action of exchange operator, as fermionic fock states; action of creation and annihilation operators, as well as, of number operator can be shown. Further, after proving using Slater determinant that number of particles in each of the states can be either 0 or 1 for a fermionic fock state, it can be shown that action of creation and annihilation operators will be different from that of bosonic fock states. And that action of number operator will give either 0 or 1 as eigenvalues, can also be shown. (Hence a link to Pauli exclusion principle can be mentioned.)

The portion in wikipedia under the heading Energy eigenstates: is not true. If the system consists of non-interacting particles, then the Hamiltonian can be shown to commute with particle number operator. On the other hand, if the particles interact among themselves, then the Hamiltonian does not not commute with the particle number operator. So this portion can be edited and the reason of fock states, not being energy eigenstates, will be added.

Advanced quantum mechanics by Franz Schwabl; ISBN: 978-3-540-85062-5.
Relativistic Quantum Mechanics and Field Theory by Franz Gross; ISBN: 978-0-471-35386-7.
Condensed Matter Field Theory by Altland, A. and Simons B. D., 2010, Chapter 2. ISBN-10: 0521769752; ISBN-13: 978-0521769754.
The symmetric and antisymmetric behaviour of states under operation of exchange operator; indistinguishability and need of fock space; use of boson creation & annihilation operators; use of fermion creation & annihilation operators; from this reference of Lecture on Multiparticle systems: indistinguishability and consequences ^[3].
Optical Coherence and Quantum Optics by Leonard Mandel and Emil Wolf; 1995; Page 478, Chapter 10; ISBN: 0521417112.
Introduction to Many-body Quantum Theory in Condensed Matter Physics by Henrik Bruus and Karsten Flensberg, 2003; Chapter 1, Page 10.
Quantum Mechanics (Non-relativistic theory), by L. D. Landau and E. M. Lifschitz, Chapter 9; ISBN-13: 978-0750635394; ISBN-10: 0750635398.
Ideas on identical particles from the chapter named Systems of identical particles of Quantum Mechanics (Vol 2) by C. Cohen-Tannoudji, Bernard Diu, Frank Laloe; ISBN: 978-0-471-16435-7.

Email id : indranil.roy@tifr.res.in

Indranil1993 (talk) 18:35, 12 October 2014 (UTC)