ISSN:
1572-9524
Keywords:
Quantum mechanics
;
dynamical system
;
energy level crossing
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract From the eigenvalue equationH λ \ψ n (λ)〉 =E n (λ)\ψ n (λ)〉 withH λ ≡H 0 +λV one can derive an autonomous system of first order differential equations for the eigenvaluesE n (λ) and the matrix elementsV mn (λ) whereλ is the independent variable. To solve the dynamical system we need the initial valuesE n (λ = 0) and \ψ n (λ = 0)〉. Thus one finds the “motion” of the energy levelsE n (λ). We discuss the question of energy level crossing. Furthermore we describe the connection with the stationary state perturbation theory. The dependence of the survival probability as well as some thermodynamic quantities onλ is derived. This means we calculate the differential equations which these quantities obey. Finally we derive the equations of motion for the extended caseH λ =H 0 +λV 1 +λ 2 V 2 and give an application to a supersymmetric Hamiltonian.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00661855
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