A new path integral representation for the solutions of the
Schrödinger, heat and stochastic Schrödinger equations
2002 ◽
Vol 132
(2)
◽
pp. 353-375
◽
Keyword(s):
Solutions to the Schrödinger, heat and stochastic Schrödinger equation with rather general potentials are represented, both in x- and p-representations, as integrals over the path space with respect to σ-finite measures. In the case of x-representation, the corresponding measure is concentrated on the Cameron–Martin Hilbert space of curves with L2-integrable derivatives. The case of the Schrödinger equation is treated by means of a regularization based on the introduction of either complex times or continuous non-demolition observations.
2004 ◽
Vol 7
(2)
◽
pp. 183-204
◽
1997 ◽
Vol 09
(08)
◽
pp. 907-920
◽
1996 ◽
Vol 29
(24)
◽
pp. 7837-7853
◽
2005 ◽
Vol 17
(10)
◽
pp. 1143-1207
◽
Keyword(s):