Can the Momentum of an Electron Be Determined from Its Wavefunction?

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In summary, the conversation discusses the confusion surrounding the relationship between wavefunction and momentum in quantum mechanics. The question asks if the momentum of an electron can be determined from its given wavefunction, to which the response points out that in quantum mechanics, the wavefunction can be in a superposition of momentum eigenstates and the momentum can only be determined through measurement.
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Sasuke
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wavefunction/momentum confusion

Homework Statement


Given a wavefunction [tex]\Psi[/tex]=Asin(cx) of an electron can i find it's momentum?


Homework Equations


Thats what i don't know.

The Attempt at a Solution


Wave function squared is the probability if finding the particle. So I'm given the probability of finding a particle in space how do i find momentum when momentum is dependant on time but the given wavefunction is not?
 
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  • #2
What makes you think that the electron even has a definite momentum? In quantum mechanics, a wavefunction can be in a superposition of momentum eigenstates, and if the momentum is measured, each momentum eigenvalue will have some probability of being observed.

What does the question really say? (word for word)
 

FAQ: Can the Momentum of an Electron Be Determined from Its Wavefunction?

What is wavefunction/momentum confusion?

Wavefunction/momentum confusion is a common misunderstanding in quantum mechanics. It refers to the mistaken belief that the wavefunction of a particle directly represents its momentum, when in reality the wavefunction is a mathematical representation of the probability of finding a particle in a particular state.

How does this confusion arise?

This confusion often arises because the wavefunction is often described in terms of its amplitude and wavelength, which are similar to the properties of a classical wave. However, unlike a classical wave, the wavefunction does not have a physical meaning and cannot be directly measured.

What is the difference between wavefunction and momentum?

The wavefunction is a mathematical description of the probability of finding a particle in a particular state, while momentum is a physical quantity that describes the motion of a particle. The wavefunction is related to the momentum of a particle through the principles of quantum mechanics, but it is not a direct representation of momentum.

Can the wavefunction and momentum be measured simultaneously?

No, according to the Heisenberg uncertainty principle, the wavefunction and momentum of a particle cannot be measured simultaneously with complete accuracy. This means that while the wavefunction can give us information about the probability of a particle's momentum, we cannot know both quantities at the same time.

How can one avoid wavefunction/momentum confusion?

The best way to avoid this confusion is to have a clear understanding of the principles of quantum mechanics and the difference between the wavefunction and momentum. It is also important to keep in mind that the wavefunction is a mathematical tool used to describe the behavior of particles at the quantum level, and should not be interpreted as a physical quantity.

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