The infinite square well potential and the evolution operator method for the purpose of overcoming misconceptions in quantum mechanics

2014 ◽  
Vol 35 (2) ◽  
pp. 025001 ◽  
Author(s):  
L M Arévalo Aguilar ◽  
F Velasco Luna ◽  
C Robledo-Sánchez ◽  
M L Arroyo-Carrasco
Keyword(s):  
Quantum Mechanics ◽  
Evolution Operator ◽  
Operator Method ◽  
Square Well

INVARIANT EIGEN-OPERATOR METHOD OF DERIVING ENERGY-LEVEL GAP FOR NONCOMMUTATIVE QUANTUM MECHANICS

2005 ◽  
Vol 20 (09) ◽  
pp. 691-698 ◽  
Author(s):  
SI-CONG JING ◽  
HONG-YI FAN
Keyword(s):  
Quantum Mechanics ◽  
Energy Level ◽  
Operator Method ◽  
Simple Algebra ◽  
New Method ◽  
Noncommutative Quantum Mechanics ◽  
Noncommutative Quantum

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.

Theory of Spontaneous and Stimulated Emission in Two Band Intrinsic Semiconductor

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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