A full quantum analysis of the Stern–Gerlach experiment using the evolution operator method: analyzing current issues in teaching quantum mechanics

We propose a new method to derive energy-level gap for Hamiltonians in the context of noncommutative quantum mechanics (NCQM). This method relies on finding invariant eigen-operators whose commutators with Hamiltonian are still the operators themselves but with some eigenvalue-like coefficients, which correspond to the energy-level gaps of the systems. Based on this method, only after some simple algebra, we derive the energy-level gaps for several important systems in NCQM, and most of these results have not been reported in literature so far.

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Theory of Spontaneous and Stimulated Emission in Two Band Intrinsic Semiconductor

Modern Physics Letters B ◽

10.1142/s0217984997000608 ◽

1997 ◽

Vol 11 (11) ◽

pp. 493-502

Author(s):

Vladislav Cheltsov

Keyword(s):

Evolution Operator ◽

Chemical Potential ◽

Operator Method ◽

Single Mode ◽

Excitation Level ◽

Stimulated Emission ◽

Quasi Equilibrium ◽

Intrinsic Semiconductor ◽

Einstein Distribution ◽

Bose Einstein

The behavior of a single mode of radiation field coupled to an excited two band intrinsic semiconductor has been investigated with the help of the commutator version of evolution operator method. As dependent on the excitation level three states of the field has been shown to exist: the equilibrium with the number of photons determined by the Bose–Einstein distribution with nonzero chemical potential; the quasi-equilibrium with the average number of photons equal to unity and accompanied by fluctuations; the state of photon avalanche.

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Time-evolution operator method for non-Markovian density matrix propagation in time and space representation: Application to laser association of OH in an environment

Physical Review A ◽

10.1103/physreva.79.013415 ◽

2009 ◽

Vol 79 (1) ◽

Cited By ~ 6

Author(s):

G. K. Paramonov ◽

Peter Saalfrank

Keyword(s):

Density Matrix ◽

Time Evolution ◽

Evolution Operator ◽

Operator Method ◽

Space Representation ◽

Time And Space ◽

Time Evolution Operator ◽

Laser Association

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Quantum mechanics/molecular mechanics methods can be more accurate than full quantum mechanics in systems involving dispersion correlations

Physical Chemistry Chemical Physics ◽

10.1039/c0cp02957b ◽

2011 ◽

Vol 13 (22) ◽

pp. 10520 ◽

Cited By ~ 16

Author(s):

W. M. C. Sameera ◽

Feliu Maseras

Keyword(s):

Quantum Mechanics ◽

Molecular Mechanics ◽

Full Quantum

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On the derivation of the Pauli and van Hove master equations

Canadian Journal of Physics ◽

10.1139/p78-161 ◽

1978 ◽

Vol 56 (9) ◽

pp. 1204-1217 ◽

Cited By ~ 4

Author(s):

K. M. van Vliet

Keyword(s):

Projection Operator ◽

Evolution Operator ◽

Random Phase ◽

Stochastic Theory ◽

Operator Method ◽

Original Method ◽

Von Neumann ◽

Projection Operator Method ◽

Von Neumann Equation ◽

Pauli Master Equation

We discuss the derivation of the Pauli master equation, based on a repeated random phase assumption, and of van Hove's result, based on an initial random phase assumption. For the former we indicate a derivation which is closer to the general approach of stochastic theory than Pauli's original method. For the van Hove result, we show that the diagonal and nondiagonal parts of the evolution operator of the Schrödinger or von Neumann equation are readily obtained by Zwanzig's projection operator method.

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