Let E(t, h) be the Fourier Integral Operator representing the parametrix of the propagator for the Schrödinger equation Qψ=ih∂tψ, Q=- 1/2h2δx + V(x), where V is a potential of quadratic growth in Rn. It is proved that E(t, h) coincides exactly with the Schwarte kernel of the propagator if and only if V is a positive quadratic form, i.e. if the corresponding physical system is a n-dimensional harmonic oscillator. © 1988 Fondazione Annali di Matematica Pura ed Applicata.
Parmeggiani, A. (1988). On the parametrix for a class of Schrödinger operators with potentials of quadratic growth. ANNALI DI MATEMATICA PURA ED APPLICATA, 152(1), 237-258 [10.1007/BF01766152].
On the parametrix for a class of Schrödinger operators with potentials of quadratic growth
Parmeggiani A.
1988
Abstract
Let E(t, h) be the Fourier Integral Operator representing the parametrix of the propagator for the Schrödinger equation Qψ=ih∂tψ, Q=- 1/2h2δx + V(x), where V is a potential of quadratic growth in Rn. It is proved that E(t, h) coincides exactly with the Schwarte kernel of the propagator if and only if V is a positive quadratic form, i.e. if the corresponding physical system is a n-dimensional harmonic oscillator. © 1988 Fondazione Annali di Matematica Pura ed Applicata.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
