what is the difference between Hamiltonian and energy in schrödinger's wave equation ?
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Answers
Answer:
The Hamiltonian is where the the system cannot be. A simple example is a ball on a hill. The Hamiltonian is the hill.
Here are the different terms:
The Hamiltonian: this is where things cannot be; technically speaking they do not have enough energy to occupy some space. For example, you cannot occupy a space occupied by another mass (say the floor, or your bed, ect..). The math for these problems is nasty stuff - so people often start by defining the Hamiltonian first, it is usually the easiest part of the problem.
The Wavefunction: this is where things are. It is the ball. Technically speaking, the Schrodinger wave equation should tell you where anything is, and the wavefunction should have all that information. That said - there is a caveat to this rule: you can’t know both the precise location and speed, at the same time. The math is such that if you know the absolute speed of something, you have no idea of where it is, and vice verse. This is a funky result of the .
The Energy: This is the energy of the object. That's total, absolute energy; i.e. everything it's got.
Answer:
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