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Model ID: 113

Solution of the Schrödinger Equation for the Hydrogen Atom

This example shows how to compute energy levels and electron orbits for the hydrogen atom. It models the atom as a 1-particle system using the stationary Schrödinger equation.

Before solving this problem in COMSOL Multiphysics, the dimension of the problem is firstly reduced from three to two by using cylindrical coordinates (rho, phi, z). The model is then set up using the PDE Coefficient axisymmetry application mode.

Solution of the Schrödinger Equation for the Hydrogen Atom Picture showing the energy levels as function of the principal quantum number (small figure), and the wave function corresponding to the fourth eigenvalue (GUI window).


Engineering Fields

  • Quantum Mechanics
  • Equation-Based Modeling
  • Benchmarking Studies

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