Bounds for Hamiltonians with arbitrary kinetic parts
arXiv:1206.5960 · doi:10.1016/j.rinp.2012.09.004
Abstract
A method is presented to compute approximate solutions for eigenequations in quantum mechanics with an arbitrary kinetic part. In some cases, the approximate eigenvalues can be analytically determined and they can be lower or upper bounds. A semiclassical interpretation of the generic formula obtained for the eigenvalues supports a new definition of the effective particle mass used in solid state physics. An analytical toy model with a Gaussian dependence in the momentum is studied in order to check the validity of the method.
Improved version with new refernces
References in corpus (8)
- Auxiliary fields as a tool for computing analytical solutions of the Schrödinger equation
- A general comparison theorem
- An upper bound for asymmetrical spinless Salpeter equations
- Some equivalences between the auxiliary field method and the envelope theory
- Semirelativistic Hamiltonians and the auxiliary field method
- Duality relations in the auxiliary field method
- Effective Mass and Energy-Mass Relationship
- Energy Band Model Based on Effective Mass