The free time-dependent Schrödinger equation in three-dimensional space is analyzed as a special case of the wave equation in five-dimensional spacetime. This approach transforms the separation of variables in the parabolic Schrödinger equation into the separation of variables in a nonparabolic equation. Then one can solve the problem using the last theorem of V. N. Shapovalov (see Differents. Uravn., No. 10, 1864 (1980)) on the necessary and sufficient conditions for the complete separation of variables. Other advantages of this approach are also discussed.
ASJC Scopus subject areas
- Physics and Astronomy(all)