![]() Thus, as long as the potential energy function is constant in time, Schrödinger’s equation is separable and all of our work studying the time-independent equation is valid, as long as we remember that these solutions are actually oscillating in time according to the description given above. It has the form of an eigenvalue' equation, H E (3.12) where H is the Hamiltonian operator H h2 2m d2 dx2 + V(x) (3.13) and Eis the eigenvalue. ![]() In fact, if we set A = 1, the temporal part of the wavefunction will have no effect on the probabilities calculated earlier in this chapter. An alternative method is proposed for deriving the time-dependent Schrdinger equation from the pictures of wave and matrix mechanics. (3.10) is known as the time-independent Schr odinger equation' (TISE), and solving it is a central problem in quantum theory.
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