We recall (from a previous post of mine) that the momentum eigenfunctions are described by the following differential equation. The momentum operator, like the Hamiltonian operator has real eigenvalues. This is because it is a physically observable quantity. ... Suppose we ask: What is the probability that if we make a measurement of the position of the state represented by |psi>, we find the value x? Since the position is an observable quantity, we can pretty much& ...
identify eigenfunction momentum operator
The momentum operator, $p=-i\frac{\partial}{\partial x}$. Apply that to the wavefunction and see what you get. For it to be an eigenfunction, it must satisfy the equation $\hat{p}\psi \propto \psi$. Then do the same for $\hat{p}^2$.
Thus there are no eigenfunctions of the momentum operator that lie in Hilbert space (which, remember, is the vector space of square-integrable functions). What happens if do the normalization integral anyway? That is, we try.
1. The problem statement, all variables and given/known data. Find the energy eigenvalues and eigenfunctions for the one-dimensional infinite square well. Calculate the matrices for the position and momentum operators,& ...
We recall (from a previous post of mine) that the momentum eigenfunctions are described by the following differential equation. The momentum operator, like the Hamiltonian operator has real eigenvalues. This is because it is a physically observable quantity. ... Suppose we ask: What is the probability that if we make a measurement of the position of the state represented by |psi>, we find the value x? Since the position is an observable quantity, we can pretty much& ...
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- Aug 27 Tue 2013 21:27
Identify Eigenfunction Momentum Operator
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Identify Eigenfunction Momentum Operator
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