Working with Three-Dimensional Rectangular Potentials
Applying the Schrödinger Equation in Three Dimensions
Calculate the Wave Function of a Hydrogen Atom Using the Schrödinger Equation

Finding the x, y, and z Equations for Three-Dimensional Free Particle Problems

At some point, your quantum physics instructor may want you to find the x, y, and z equations for three-dimensional free particle problems. Take a look at the x equation for the free particle,


You can write its general solution as


where Ay and Az are constants.



you get this for


where A= Ax Ay Az.

The part in the parentheses in the exponent is the dot product of the vectors


That is, if the vector a = (ax, ay, az) in terms of components and the vector b = (bx, by, bz), then the dot product of a and b is


So here’s how you can rewrite the

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