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!