## Exam Information

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## Sample Document Text

Here are lots of quantum mechanics questions from previous exams
that would be fair game this year:
5. (2 min) What is a quantum-mechanical wave function a function of (i.e. what are its
independent variables and how many are there)?
6. (4 min) List the conditions a wave function must satisfy in order to solve the
Schrödinger equation.
7. (6 min) Suppose cos(ax) solves the Schrödinger Equation for a particle in one
dimension.
a) From cos(ax) determine mathematically the kinetic energy as a function of
position.
b) Explain mathematically how the total energy varies with 1/a, the wavelength of
the function.
4. (2 min) Formulae for the wave function of H-like atoms look very complicated because of all the
constants that appear in order to give proper scaling. For what purpose does one need to scale the
wave functions?
8. The curve below is Psi, a solution to the Schrödinger equation for a familiar type
of potential energy function. The horizontal line is at a Psi value of 0. The
function c...

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