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jstrunk

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- When does an even potential energy result in an even and an odd solution to Time Independent Schrodinger Equation

I don't understand this statement about potential energy V(x) from Griffiths Intro to Quantum Mechanics, 3rd Ed.

Problem 2.1c: If V(x) is an even function (that is V(-x)=V(x)) then psi(x) can always be taken to be either even or odd.

psi(x) refers to a solution of the Time Independent Schrodinger Equation.

It is not clear what "psi(x) can always be taken to be either even or odd" means.

From working the examples and problems in the text, it seems what it means in practice is

a) For bound states (energy < 0), there is an even solution and an odd solution.

b) For scattering states (energy > 0), there is just one solution.

Of course, that 'one solution' may be a superposition of wave functions, I just mean you don't have to solve for

an even case and an odd case.

Is this correct?

Problem 2.1c: If V(x) is an even function (that is V(-x)=V(x)) then psi(x) can always be taken to be either even or odd.

psi(x) refers to a solution of the Time Independent Schrodinger Equation.

It is not clear what "psi(x) can always be taken to be either even or odd" means.

From working the examples and problems in the text, it seems what it means in practice is

a) For bound states (energy < 0), there is an even solution and an odd solution.

b) For scattering states (energy > 0), there is just one solution.

Of course, that 'one solution' may be a superposition of wave functions, I just mean you don't have to solve for

an even case and an odd case.

Is this correct?

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