Energy level motion and a supersymmetric Hamiltonian
W -H Steeb; S J M Brits; A J Van Tonder; W -H Steeb; Dept. of Phys., Rand Afrikaans Univ., Johannesburg, South Africa; S J M Brits; Dept. of Phys., Rand Afrikaans Univ., Johannesburg, South Africa; A J Van Tonder; Dept. of Phys., Rand Afrikaans Univ., Johannesburg, South Africa
Журнал:
Journal of Physics A: Mathematical and General
Дата:
1988-06-07
Аннотация:
From the eigenvalue equation H<sub>lambda </sub> mod psi <sub>n</sub>( lambda )>=E<sub>n</sub>( lambda ) mod psi <sub>n</sub> ( lambda )) where H<sub>lambda </sub> identical to H<sub>0</sub>+ lambda V one can derive an autonomous system of first-order differential equations for the eigenvalues E<sub>n</sub>( lambda ) and the matrix elements V<sub>mn</sub>( lambda ):=( psi <sub>m</sub>( lambda ) mod V mod psi <sub>n</sub>( lambda )) where lambda is the independent variable. To solve the dynamical system the authors need the initial values E<sub>n</sub>( lambda =0) and mod psi <sub>n</sub>( lambda =0)). Thus one finds the 'motion' of the energy levels E<sub>n</sub>( lambda ). They derive the equations of motion for the extended case H<sub>lambda </sub>=H<sub>0</sub>+ lambda V<sub>1</sub>+ lambda <sup>2</sup>V<sub>2</sub> and give an application to a supersymmetric Hamiltonian.
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