Expectation Value of Position for Even Wavefunction

[hellsteiger]

Homework Statement

Hello, I need to calculate the expectation value for position and momentum for a wavefunction that fulfills the following relation:

ψ₀(-x)=ψ₀(x)=ψ^*₀(x)

The wave function is normalised.

Homework Equations

There is also a second wave equation that is orthogonal to the first:

ψ₁=Nd₀/dx

I also need to calculate <x> and <p> for this wavefunction, also normalised.

The Attempt at a Solution

I am tempted to go ahead and say that the expectation value for position for both wavefunctions is 0, as they are both even. As for momentum I am not certain as to how i should proceed, inserting the relevant operator just seems to indicate to me momentum will be zero.

 

[hellsteiger]

Correction:

ψ1=Ndψ₀/dx

 

[hellsteiger]

I should point out that ψ₁ is actually an odd function, being the derivative of an even function, it is not even as i stated earlier.

 

[vanhees71]

Just write down the expectation values of position and momentum in terms of the wave function (the position representation of the quantum state). Then discuss the mathematics given the symmetry properties, i.e., either even or odd, of the wave functions.