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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 timedependent Schrödinger equation (3.12) We shall only spend limited time on this equation. Initially we are interested in the timeindependent 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 timedependent 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 timeindepndent Schrödinger equation (3.15) The corresponding solution to the timedependent equation is the standing wave ( 3.13 )....
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 Fall '10
 DavidJudd
 Physics, Calculus, Schrodinger Equation, de Broglie

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