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| related topics |
| {equation, function, exp} |
| {energy, state, states} |
| {state, algorithm, problem} |
| {field, particle, equation} |
| {level, atom, field} |
| {group, space, representation} |
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Ultraviolet analysis of one dimensional quantum systems
Marco Frasca
abstract: Starting from the study of one-dimensional potentials in quantum mechanics
having a small distance behavior described by a harmonic oscillator, we extend
this way of analysis to models where such a behavior is not generally expected.
In order to obtain significant results we approach the problem by a
renormalization group method that can give a fixed point Hamiltonian that has
the shape of a harmonic oscillator. In this way, good approximations are
obtained for the ground state both for the eigenfunction and the eigenvalue for
problems like the quartic oscillator, the one-dimensional Coulomb potential
having a not normalizable ground state solution and for the one-dimensional
Kramers-Henneberger potential. We keep a coupling constant in the potential and
take it running with a generic cut-off that goes to infinity. The solution of
the Callan-Symanzik equation for the coupling constant generates the harmonic
oscillator Hamiltonian describing the behavior of the model at very small
distances (ultraviolet behavior). This approach, although algorithmic in its
very nature, does not appear to have a simple extension to obtain excited state
behavior. Rather, it appears as a straightforward non-perturbative method.
- oai_identifier:
- oai:arXiv.org:quant-ph/0202067
- categories:
- quant-ph hep-th math-ph math.AP math.MP physics.atom-ph
- comments:
- 10 pages, no figures
- arxiv_id:
- quant-ph/0202067
- journal_ref:
- Nuovo Cim. B117 (2002) 867-874
- created:
- 2002-02-12
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