On the Solution of the Differential Equation (∂2∂x∂y+ax∂∂x+by∂∂y+cxy+∂∂t)P=0
- 1 March 1970
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 11 (3) , 829-831
- https://doi.org/10.1063/1.1665220
Abstract
The following solution is obtained: P(x,y,t)=e −γxy−δ P 0 (e −α x,e −β y,ε) ,where P 0(x, y, t) is the solution when the constants a, b, and c are zero, and where the time functions α, …, ε are given explicitly.Keywords
This publication has 3 references indexed in Scilit:
- Closed-Form Solution of the Differential Equation (∂2∂x∂y+ax∂∂x+by ∂∂y+cxy+∂∂t)P=0 Subject to the Initial Condition P(x, y, t = 0) = Φ(x, y)Journal of Mathematical Physics, 1969
- Solution of the Differential Equation (∂2∂x∂y+ax∂∂x+by∂∂y+cxy+∂∂t)P=0Journal of Mathematical Physics, 1967
- Exact Quantum Dynamical Solutions for Oscillator-Like SystemsPhysical Review B, 1956