Quantum Physics, Schrödinger Equation...

He never studied Taoism, have he?

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I know you can kind of pull the Schrodinger equation out of Hamilton-Jacobi theory, but you still have to make some stretches to make it quantum.

One of my friends actually did some crazy integrals and what he called "geometric relaxation" and used classical mechanics to kinda pull out the ground state solution to the hydrogen atom.

From the perspective of operators, the solutions to the Schrodinger equation are just eigenstates of the Hamiltonian, so in that sense you can "derive" it from some basic postulates about quantum mechanics, but these are made with the knowledge of the results already established and merely fitting a neater mathematical formulation to what is observed in nature.

 

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'Derivation' is not the appropriate term to use here,rather Schrodinger equation is equivalent with the equation of the quantum hamiltonian H which is constructed,invented,using an analogy with the classical situation.

 

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Man i picked to do the Schrodinger question in a resent exam it's soooo kick ass espesialy the Schrodinger equion of a particle in a sphere it takes a lot to remember some thing like that of by heart