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I mean where, at what point, at what level, do I have to start ? Do you have any experience at all with a QM course, the hydrogen atom wave functions, the ##Y_{lm}## ? If they are not the 'usual spherical harmonics' to you, I suggest you take a QM textbook and see how far you can come.mody mody said:
The variational method is a mathematical technique used to approximate the ground state energy of a quantum mechanical system. It involves choosing a trial wavefunction and using it to calculate an upper bound for the ground state energy.
The variational method is used to find an approximate solution for the Schrödinger equation, which describes the behavior of quantum systems. By choosing a trial wavefunction and calculating its energy, we can compare it to the exact energy and improve the accuracy of our approximation by adjusting the wavefunction.
The variational method allows us to obtain an approximation for the ground state energy of a system without solving the Schrödinger equation exactly. This can be useful for complex systems where an exact solution is not possible.
One limitation of the variational method is that it can only provide an upper bound for the ground state energy. Additionally, the accuracy of the approximation depends on the choice of trial wavefunction, which can be difficult to determine for some systems.
The variational method is related to other approximation techniques in quantum mechanics, such as perturbation theory and the Hartree-Fock method. It is also closely related to the calculus of variations, a mathematical framework for finding the extreme values of functions.
