Energy function - less than 0 (no solution for ). For...

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Energy function Of course the kinetic energy is , with . The sum of kinetic and potential energy can be written in the form (2.3) Actually, this form is not very convenient for quantum mechanics. We rather work with the so- called momentum variable . Then the energy functional takes the form (2.4) Simple example We can define all these concepts (velocity, momentum, potential) in one dimensionas well as in three dimensions. Let us look at the example for a barrier (2.5) We can't find a solution for
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Unformatted text preview: less than 0 (no solution for ). For energy less then the particles can move left or right from the barrier, with constant velocity, but will make a hard bounce at the barrier (sign of is not determined from energy). For energies higher than particles can move from one side to the other, but will move slower if they are above the barrier. The energy expressed in terms of and is often called the (classical) Hamiltonian, and will be shown to have a clear quantum analog....
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