Question

Derive relation between Hamiltonian operator and Laplacian operator?

Answer 1

Answer:

The Laplacian operator is called an operator because it does something to the function that follows: namely, it produces or generates the sum of the three second-derivatives of the function. ... It is a general principle of Quantum Mechanics that there is an operator for every physical observable

Since we have shown that the Hamiltonian operator is hermitian, we have the important result that all its energy eigenvalues must be real. In fact the operators of all physically measurable quantities are hermitian, and therefore have real eigenvalues.

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