dorsal/arxiv
View SchemaComplex Square Well --- A New Exactly Solvable Quantum Mechanical Model
| Authors | Carl M. Bender, Stefan Boettcher, H. F. Jones, Van M. Savage |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9906057 |
| URL | https://arxiv.org/abs/quant-ph/9906057 |
| DOI | 10.1088/0305-4470/32/39/305 |
| Journal | J.Phys.A32:6771-6781,1999 |
Abstract
Recently, a class of PT-invariant quantum mechanical models described by the non-Hermitian Hamiltonian $H=p^2+x^2(ix)^\epsilon$ was studied. It was found that the energy levels for this theory are real for all $\epsilon\geq0$. Here, the limit as $\epsilon\to\infty$ is examined. It is shown that in this limit, the theory becomes exactly solvable. A generalization of this Hamiltonian, $H=p^2+x^{2M}(ix)^\epsilon$ (M=1,2,3,...) is also studied, and this PT-symmetric Hamiltonian becomes exactly solvable in the large-\epsilon limit as well. In effect, what is obtained in each case is a complex analog of the Hamiltonian for the square well potential. Expansions about the large-\epsilon limit are obtained.
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"abstract": "Recently, a class of PT-invariant quantum mechanical models described by the\nnon-Hermitian Hamiltonian $H=p^2+x^2(ix)^\\epsilon$ was studied. It was found\nthat the energy levels for this theory are real for all $\\epsilon\\geq0$. Here,\nthe limit as $\\epsilon\\to\\infty$ is examined. It is shown that in this limit,\nthe theory becomes exactly solvable. A generalization of this Hamiltonian,\n$H=p^2+x^{2M}(ix)^\\epsilon$ (M=1,2,3,...) is also studied, and this\nPT-symmetric Hamiltonian becomes exactly solvable in the large-\\epsilon limit\nas well. In effect, what is obtained in each case is a complex analog of the\nHamiltonian for the square well potential. Expansions about the large-\\epsilon\nlimit are obtained.",
"arxiv_id": "quant-ph/9906057",
"authors": [
"Carl M. Bender",
"Stefan Boettcher",
"H. F. Jones",
"Van M. Savage"
],
"categories": [
"quant-ph",
"cond-mat",
"hep-th",
"math-ph",
"math.MP"
],
"doi": "10.1088/0305-4470/32/39/305",
"journal_ref": "J.Phys.A32:6771-6781,1999",
"title": "Complex Square Well --- A New Exactly Solvable Quantum Mechanical Model",
"url": "https://arxiv.org/abs/quant-ph/9906057"
},
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