Multiple symmetries

In quantum mechanics there are many occasions where quantum states are written as products of two or more functions, each with its own set of variables. for instance, spin-dependent wave functions Ψ[x _i , y _i , z _i , s _i ] are written as ψ [x _i , y _i , z _i ] ø [s _i ], or linear combinations thereof. In the Born-Oppenheimer approximation the electronic and vibrational wave functions are multiplied together to make the “vibronic” wave function