Separating variables in general

Assume that a set of variables can be found where the Hamiltonian operator H for two particles/variables can be separated into two independent terms, with each only depending on one particle/variable  

Assume furthermore that the Schrodinger equation for one particle/variable can be solved (exactly or approximately)  

The solution to the two-particle problem can then be composed of solutions of one-variable Schrddinger equations. 

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