ATM-007 · Foundations of quantum mechanics Sample material

Foundations of quantum mechanics. The Schrödinger equation

The basic postulates of quantum mechanics: the wave function and its properties, operators of physical quantities, the Hamiltonian operator, the time-dependent and stationary Schrödinger equations.

Estimated time: 3 h 3 activities

Learning objective

Explain the physical meaning and the standard conditions of the wave function.
Learn to work with the basic operators (coordinate, momentum, energy, angular momentum).
Write the time-dependent and stationary Schrödinger equations and understand their meaning.
Derive the quantization of energy in an infinitely deep potential well.

Expected outcomes

Normalizes a wave function and calculates the probability of finding the particle in a given region.
Can determine the eigenfunctions and eigenvalues of an operator.
Can write the Hamiltonian operator and the Schrödinger equation for a given potential.
Calculates the energy of a particle in an infinitely deep well, $E_n = n^2h^2/(8mL^2)$.

Interactive modelA particle in a potential well: wavefunctions

Activities

Lecture
Lecture · 1 h 20 min · required
Foundations of quantum mechanics.
Practice · 1 h 20 min · required
Final test
Test · 20 min · required · pass ≥ 70%

Completion conditions

  • Lecture
  • Foundations of quantum mechanics.
  • Final test — at least 70%