Activities

Small Group Activity

30 min.

$|\pm\rangle$ Forms an Orthonormal Basis

Student explore the properties of an orthonormal basis using the Cartesian and $S_z$ bases as examples.

Cartesian Basis $S_z$ basis completeness normalization orthogonality basis Quantum Mechanics
Found in: Quantum Fundamentals, None course(s) Found in: Completeness Relations sequence(s)

Problem

Normalization of Quantum States

Show that if a linear combination of ring energy eigenstates is normalized, then the coefficients must satisfy \begin{equation} \sum_{m=-\infty}^{\infty} \vert c_m\vert^2=1 \end{equation}

Found in: Central Forces course(s)

Small White Board Question

5 min.

DELETE Normalization of the Gaussian for Wavefunctions

The Gaussian \begin{equation} {\cal P}(x)=\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{(x-x_0)^2}{2\sigma^2}} \end{equation} is normalized so that the area under the curve is equal to one. If this Gaussian represents the probability density for a free quantum mechanical particle, what is a possible wavefunction?

Found in: Periodic Systems course(s) Found in: Fourier Transforms and Wave Packets sequence(s)

\(|\pm\rangle\) Forms an Orthonormal Basis

Normalization of Quantum States

DELETE Normalization of the Gaussian for Wavefunctions