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Dec
10
answered Beyond WKB approximation for energies
Dec
6
awarded  Necromancer
Dec
3
answered Other Gross-Neveu like theories?
Nov
27
answered Hawking Radiation from the WKB Approximation
Nov
27
awarded  Caucus
Nov
22
answered Constructing Supersymmetric Lagrangians
Nov
20
comment Finding the energy levels of an electron in a plane perpendicular to a uniform magnetic field
If I may add, if you write $a = x+ip$ and $a^{\dagger} = x-ip$, you get the harmonic oscillator Hamiltonian in the usual representation, but the harmonic osillator coordinates $x$ and $p$ are not the original coordinates that you started with.
Nov
20
comment Finding the energy levels of an electron in a plane perpendicular to a uniform magnetic field
If you substitute the expressions of $a$ and $a^{\dagger}$ given in the answer in the Hamiltonian $H=\hbar\omega(a a^{\dagger}+\frac{1}{2})$ you get the Hamiltonian you started with expressed in terms of $X$ and $P$.
Nov
20
comment Finding the energy levels of an electron in a plane perpendicular to a uniform magnetic field
The Hamiltonian expressed in terms of the creation and annihilation operators has exactly the form of the harmonic oscillator Hamiltonian. Thus the energy levels are exactly equal to those of the harmonic oscillator, however with infinite degeneracy per level (The harmonic oscillator energy levels are nondegenerate). The advantage of using this method is that it allows an algebraic solution of the energy levels (i.e. without solving differential equations), please see the quantum harmonic oscillator Wikipedia page: en.wikipedia.org/wiki/Quantum_harmonic_oscillator
Nov
20
answered Finding the energy levels of an electron in a plane perpendicular to a uniform magnetic field
Nov
19
comment What are the solution spaces of Nonlinear Schrödinger equations?
@Arnold The following work by Forger and Romero establishes the equivalence betwee Crnkovic-Witten-Zuckerman and the Peierls brackets and relates them to the multisymplectic approach arxiv.org/pdf/math-ph/0408008.pdf
Nov
19
comment Interacting representation of the Poincaré group
cont., In 4D scalar theory, in the free case, the (free) Poincaré generators can be expressed in terms the field's creation and anihilation operators and their action on the corresponding (free) Fock space is completely known. In addition approximate representations can be constructed order by order in perturbation theory in which the interacting Poincaré generators will have higher polynomial dependence on the creation and anihilation operators (acting on the free Fock space), but an exact representation is not known.
Nov
19
comment Interacting representation of the Poincaré group
@BGal One can easily find an interaction term, and construct the expressions of the interacting algebra in terms of the field variables. For example in a scalar field theory \mathcal{H} = \lambda \phi^4 is a possible interaction term, and it is easy to exactly construct interacting Poincaré generators in terms of the field and its derivatives. Finding a representation on the other hand would mean to find a Hilbert space on which the action of the interacting Poincaré generators is completely known.
Nov
18
comment What are the solution spaces of Nonlinear Schrödinger equations?
@Arnold, please see the Crncovic-Witten and Zuckerman's articles given in Urs Schreiber's answer physics.stackexchange.com/questions/26883/…. The Crncovic-Witten's link is not working, but you can find their article in the book: books.google.co.il/…
Nov
18
comment What are the solution spaces of Nonlinear Schrödinger equations?
@Arnold, Please see for example fiz.uni.opole.pl/pgar/documents/IJMPA87.pdf by Piotr Garbaczewski
Nov
18
answered Interacting representation of the Poincaré group
Nov
12
revised Aharonov-Bohm Effect and Integer Quantum Hall Effect
edited body
Nov
12
answered Aharonov-Bohm Effect and Integer Quantum Hall Effect
Nov
6
revised Symmetries of spacetime and objects over it
edited body
Nov
6
revised Symmetries of spacetime and objects over it
added 372 characters in body