Question

Suppose we have an electron with (unnormalized) wave function, where Ψ = 2x + 3y. If we measure the momentum of the electron, what is the probability that we find?

1) Cannot be determined
2) 2x + 3y
3) 2
4) 3

Answer 1

The probability of finding the electron with a specific momentum cannot be determined from the given wave function Ψ = 2x + 3y, as this information is incomplete without a Fourier transform into momentum space.

Step-by-step explanation:

The question is related to quantum mechanics and the concept of wave functions in physics. When we measure the momentum of an electron, we are dealing with quantum mechanical probabilities. The given wave function Ψ = 2x + 3y represents the state of the electron, but it doesn't directly give us probabilities for momenta. According to the principles of quantum mechanics, the probability of finding an electron in a specific state is related to the square of the magnitude of the wave function. However, this particular wave function Ψ does not correspond to a specific momentum eigenstate, and without additional information or context, such as how the wave function expands in terms of momentum eigenfunctions, we cannot determine the probability of finding the electron with a particular momentum. Instead, the wavefunction provides information about the spatial distribution of the electron's probability density.

In this case, the correct answer would be (1) Cannot be determined, because the question does not provide enough information to calculate the probability of finding the electron with a specific momentum. To find such probabilities we would need to take the Fourier transform of the spatial wave function to get the wave function in momentum space, and then calculate the probabilities from that momentum-space wave function.