JCP321H5 Lecture 5: time independent schrodinger equation
Document Summary
A simpler form of the schrodinger equation that describes the wave function as a standing wave. A neater form of this equation can be found by taking the statement for time evolution and subbing it into the above, and then we get this: After a bit of algebra, we get this: Where h is the hamiltonian and e is some energy constant. The e constant is important because it describes the energy eigenvalues at which a solution exists. The time independent schrodinger equation gives solutions for a stationary state (standing wave) or orbital. Relevance a fundamental quantum mechanical approximation describing the translational motion of a single particle. How does it work? confined inside an infinitely deep well from which it cannot escape. Here"s what this particle in a box looks like: Since the particle can"t escape from the well, the wave function reduces to the following:
