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# 13: Variational Methods

• 13.1: Variational Principle
The variational principle states, quite simply, that the ground-state energy is always less than or equal to the expectation value of H calculated with the trial wavefunction
• 13.2: Helium Atom
A helium atom consists of a nucleus of charge +2e surrounded by two electrons. Let us attempt to estimate its ground-state energy.
• 13.3: Hydrogen Molecule Ion
The hydrogen molecule ion consists of an electron orbiting about two protons, and is the simplest imaginable molecule. Let us investigate whether or not this molecule possesses a bound state: that is, whether or not it possesses a ground-state whose energy is less than that of a hydrogen atom and a free proton.
• 13.E: Variational Methods (Exercises)

# Contributors

• Richard Fitzpatrick (Professor of Physics, The University of Texas at Austin)

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