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One approach to solve the Schrodinger equation is to use separation of variables: the solution is composed of a time dependant and space dependant component. When we go through the math, we get a time dependent LHS equal to a space dependant RHS, which means they must both be equal to a separation constant E.

We know that E is the total energy of the system. Could someone explain why that is? I know the answer has to do with the Hamiltonian operator, but I have trouble understanding this concept and explaining it to others.

Thank you.

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# How do we know E is energy in the time-independent Schrodinger eq

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