Learning objectives¶

Learning goals

After following this course you will be able:

to use the uncertainty principle, quantum measurement, quantum tunnelling, and zero point energy to predict how objects behave differently in quantum mechanics than in classical mechanics.
to calculate the probability of measurement outcomes, the expectation values of observables, and be able to write down the form of the wavefunction after a measurement.
to find the eigenstates and eigenenergies for specific time-independent Hamiltonians, and use these eigenstates to calculate expectation values and the probability of measurement outcomes.
to calculate the time dependence of the wavefunction and of expectation values as a function of time.
to write down the boundary conditions for the wavefunction for step-function 1-dimensional potentials. The student will be able to use these to calculate transmission and reflection coefficients.
to use the generic uncertainty principle to calculate uncertainties in observables.
to explain why wavefunctions and operators in quantum mechanics need to satisfy specific mathematical requirements.
to use Dirac notation to express quantum states and expectation values.
to calculate commutators of quantum mechanical operators.
Given a wavefunction for a quantum state expressed in one basis (for example, position basis), the student will be able to transform this into a wavefunction in a different basis (for example, momentum basis).
to calculate eigenfunctions, expectation values, and operators in vector and matrix representation.

In these notes our aim is to provide learning materials which are:

self-contained
easy to modify and remix, so we provide the full source, including the code
open for reuse: see the license below.

Whether you are a student taking this course, or an instructor reusing the materials, we welcome all contributions, so check out the course repository, especially do let us know if you see a typo!