Central Forces 2021
- Practice time evolution
- To calculate quantum probabilities in Dirac and Wavefunction notation
- To visualize how wave wavefunctions depend on time after time evolution
- To notice that not all probabilities of operators will depend on time
What students learn
- Practice time evolution
- To calculate quantum probabilities in Dirac and Wavefunction notation
- To visualize how wave wavefunctions depend on time after time evolution
- To notice that not all probabilities of operators will depend on time
Consider a quantum particle on a ring. At \(t=0\), the particle is in state:
\begin{equation*}
\left|{\Phi(t=0)}\right\rangle =\frac{7i}{10}\left|{-2}\right\rangle -\frac{1}{2}\left|{-1}\right\rangle +\frac{1}{2}\left|{0}\right\rangle -\frac{1}{10}\left|{2}\right\rangle
\end{equation*}
- Find \(\left|{\Phi(t)}\right\rangle \)
- Calculate the probability that you measure the \(z\)-component of the angular momentum to be \(-2\hbar\) at time \(t\). Is it time dependent?
- Calculate the probability that you measure the energy to be \(\frac{2\hbar^2}{I}\) at time \(t\). Is it time dependent?
- Editor
- dustin
- Author Information
- Corinne Manogue, Kerry Browne, Elizabeth Gire, Mary Bridget Kustusch, David McIntyre, Dustin Treece
- Keywords
- central forces quantum mechanics eigenstates eigenvalues angular momentum time dependence hermitian operators probability degeneracy quantum measurements
- Prerequisite
Knowledge
-
- Familiarity with the postulates of quantum mechanics, particularly those having to do with measurement
- The energy and angular momentum eigenstates and eigenvalues of a particle confined to a ring
- Calculating probabilities using Dirac “bra-ket” and wavefunction notation
- Familiarity with time evolution in quantum mechanics
- Learning Outcomes
-
- Publication Status
- Published
- Publication Date
- May 22, 2026, 12:25 p.m.