Physics – Condensed Matter
Scientific paper
1995-01-18
J. Math. Phys. 36, 2313-2323 (1995)
Physics
Condensed Matter
14 pages, RevTeX 3.0, AMSfonts, 1 Figure available upon request from the Authors, to appear in J. Math. Phys. May 1995. Change
Scientific paper
10.1063/1.531040
The capabilities of the functional-analytic and of the functional-integral approach for the construction of the Hamiltonian as a self-adjoint operator on Hilbert space are compared in the context of non-relativistic quantum mechanics. Differences are worked out by taking the one-dimensional hydrogen atom as an example, that is, a point mass on the Euclidean line subjected to the inverse-distance potential. This particular choice is made with the intent to clarify a long-lasting discussion about its spectral properties. In fact, for the four-parameter family of possible Hamiltonians the corresponding energy-dependent Green functions are derived in closed form. The multiplicity of Hamiltonians should be kept in mind when modelling certain experimental situations as, for instance, in quantum wires.
Fischer Werner
Leschke Hajo
Mueller Peter
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