Particles in an energy eigenstate not moving?

[sheelbe999]

I'm really struggling with this one guys, the question is:

Explain why a particle which is in an energy eigenstate cannot be moving in the
classical sense.

 

[Fredrik]

What you need to know to answer this is a) the interpretation of a wavefunction, and b) how a wavefunction changes with time. (If you know that the state at t=0 is f, then what is it at arbitrary t? f(t)=(something)f, right?).

(This should probably be in the homework forum).

 

[sheelbe999]

thanks and will move it

henry

 

[Matterwave]

Hints: This has to do with "stationary states".

What is a prerequisite for a stationary state? What do stationary states imply for expectation values?

 

[paranormal]

A particle in an energy eigenstate cannot be moving in the classical sense because it is described by a single, well-defined energy level. In classical mechanics, a particle's energy is directly related to its velocity, with higher energy corresponding to higher velocity. However, in quantum mechanics, the energy of a particle is quantized and can only take on certain discrete values.

When a particle is in an energy eigenstate, it means that it has a definite energy value and is not in a state of superposition, where it could have multiple energy values at the same time. This means that the particle's energy cannot change, and therefore, its velocity cannot change either.

Furthermore, the concept of a particle "moving" in the classical sense is based on the idea of a definite position and trajectory. However, in quantum mechanics, the position of a particle is described by a wave function, which gives the probability of finding the particle at a certain position. This means that the particle does not have a well-defined position at any given time, and therefore, it cannot be said to be "moving" in the same way as a classical particle.

In summary, a particle in an energy eigenstate cannot be moving in the classical sense because its energy is quantized and cannot change, and its position is described by a probability distribution rather than a definite trajectory.