THE FUNCTIONAL INTEGRAL FOR QUANTUM-SYSTEMS WITH HAMILTONIANS UNBOUNDED FROM BELOW

被引：22

作者：

CARREAU, M

FARHI, E

GUTMANN, S

MENDE, PF

机构：

[1] MIT,DEPT PHYS,CAMBRIDGE,MA 02139

[2] MIT,DEPT MATH,CAMBRIDGE,MA 02139

[3] NORTHEASTERN UNIV,DEPT MATH,BOSTON,MA 02115

来源：

ANNALS OF PHYSICS | 1990年 / 204卷 / 01期

关键词：

D O I：

10.1016/0003-4916(90)90125-8

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A quantum system with a self-adjoint Hamiltonian has a well-defined unitary time evolution operator even if there is no ground state. However, if the spectrum of the Hamiltonian is unbounded from below, the Brownian (or imaginary time) functional integral may diverge for all times. Working in one-dimensional non-relativistic quantum mechanics with potentials which are unbounded from below at infinity and at the origin, we show how to regulate the Brownian functional integral, analytically continue to quantum mechanical time, and then remove the cutoff to obtain the quantum Green's function associated with any self-adjoint Hamiltonian. Our constructions illustrate the equivalence of the operator and functional integral approaches to quantum mechanics. © 1990.

引用

页码：186 / 207

页数：22

共 11 条

[1]

Reed, Simon, Methods of Modern Mathematical Physics. II. Fourier Analysis, Self-Adjointness, (1975)

[2]

Feynman, Hibbs, Quantum Mechanics and Path Integrals, (1965)

[3]

Breiman, Probability, (1968)

[4]

ItA, McKean, Diffusion Processes and Their Sample Paths, (1965)

[5]

Clark, Menikoff, Sharp, Phys. Rev. D, 22, (1980)

[6]

Farhi, Gutmann, Functional Integral on the Half-Line, (1989)

[7]

Farhi, Gutmann, THE FUNCTIONAL INTEGRAL ON THE HALF-LINE, International Journal of Modern Physics A, 5, (1990)

[8]

Edwards, Gulyaev, Path Integrals in Polar Co-ordinates, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 279, (1964)

[9]

Peak, Inomata, J. Math. Phys., 10, (1969)

[10]

Case, Phys. Rev., 80, (1950)

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