Potentials and bound states

Journal Article · Wed Mar 01 00:00:00 EST 1995 · American Journal of Physics; (United States)

DOI:https://doi.org/10.1119/1.17935· OSTI ID:6853849

Buell, W F ^[1]; Shadwick, B A ^[2]

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1. Department of Physics, The University of Texas at Austin, Austin, Texas 78712-1081 (United States)
2. Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712-1081 (United States)

We discuss several quantum mechanical potential problems, focusing on those which highlight commonly held misconceptions about the existence of bound states. We present a proof, based on the variational principle, that certain one dimensional potentials always support at least one bound state, regardless of the potential's strength. We examine arguments concerning the existence of bound states based on the uncertainty principle and demonstrate, by explicit calculations, that such arguments must be viewed with skepticism.

• DOE Contract Number: FG05-80ET53088
• OSTI ID: 6853849
• Journal Information: American Journal of Physics; (United States), Vol. 63:3; ISSN 0002-9505
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUND STATE
POTENTIAL ENERGY
EIGENSTATES
HAMILTONIANS
SCHROEDINGER EQUATION
UNCERTAINTY PRINCIPLE
VARIATIONAL METHODS
WAVE FUNCTIONS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
ENERGY
EQUATIONS
FUNCTIONS
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
WAVE EQUATIONS
661300* - Other Aspects of Physical Science- (1992-)