The Schrödinger Equation

The Schrödinger Equation - The...

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The Schrödinger Equation In 1925, Erwin Schrödinger and Werner Heisenberg independently developed the new quantum theory. Schrödinger's method involves partial differential equations, whereas Heisenberg's method employs matrices; however, a year later the two methods were shown to be mathematically equivalent. Most textbooks begin with Schrödinger's equation, since it seems to have a better physical interpretation via the classical wave equation. Indeed, the Schrödinger equation can be viewed as a form of the wave equation applied to matter waves. The Time-Independent Schrödinger Equation Here we follow the treatment of McQuarrie [ 1 ], Section 3-1. We start with the one- dimensional classical wave equation, (10) By introducing the separation of variables (11) we obtain (12) If we introduce one of the standard wave equation solutions for such as (the constant can be taken care of later in the normalization), we obtain (13) Now we have an ordinary differential equation describing the spatial amplitude of the
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The Schrödinger Equation - The...

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