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Unformatted text preview: (3.9) Using this we can guess a wave equation of the form (3.10) Actually using the definition of energy when the problem includes a potential, (3.11) (when expressed in momenta, this quantity is usually called a "Hamiltonian") we find the time-dependent Schrödinger equation (3.12) We shall only spend limited time on this equation. Initially we are interested in the time-independent Schrödinger equation, where the probability is independent of time. In order to reach this simplification, we find that must have the form (3.13) If we substitute this in the time-dependent equation, we get (using the product rule for differentiation) (3.14) Taking away the common factor we have an equation for that no longer contains time, the time-indepndent Schrödinger equation (3.15) The corresponding solution to the time-dependent equation is the standing wave ( 3.13 )....
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This note was uploaded on 11/09/2011 for the course PHY PHY2053 taught by Professor Davidjudd during the Fall '10 term at Broward College.
- Fall '10