The Time - The Time-Dependent Schrdinger Equation We are...

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The Time-Dependent Schrödinger Equation We are now ready to consider the time-dependent Schrödinger equation. Although we were able to derive the single-particle time-independent Schrödinger equation starting from the classical wave equation and the de Broglie relation, the time-dependent Schrödinger equation cannot be derived using elementary methods and is generally given as a postulate of quantum mechanics. It is possible to show that the time- dependent equation is at least reasonable if not derivable, but the arguments are rather involved (cf. Merzbacher [ 2 ], Section 3.2; Levine [ 3 ], Section 1.4). The single-particle three-dimensional time-dependent Schrödinger equation is (21) where is assumed to be a real function and represents the potential energy of the system (a complex function will act as a source or sink for probability, as shown in Merzbacher [ 2 ], problem 4.1). Wave Mechanics is the branch of quantum mechanics with equation ( 21 ) as its dynamical law. Note that equation (
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The Time - The Time-Dependent Schrdinger Equation We are...

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