"Distribution" of a particle in different situations

In summary: , such as the fact that electrons in a current are always moving and that a free electron can only exist in a vacuum.but certainly there are other important differences, such as the fact that electrons in a current are always moving and that a free electron can only exist in a vacuum.
  • #1
davidge
554
21
I was thinking about the "distribution" of a particle in space in different situations. An electron bound in a atom have a wave function that is broad.

What about the broadness of the wave function of conduction electrons in a wire? Or doesn't it even make sense to quantum-mechanicaly speak of conduction electrons in a wire?

What about the broadness of the wave function of a free electron? By free I mean an electron that is not interacting with any nearby particles or "classical" fields. (I know that just saying nearby is vague (How nearby?), but I hope you understand what I mean.)

So I was trying to answer myself the two questions above, and I started by thinking this way:

The time evolution of a wave function is governed by the hamiltonian of the system and I guess the hamiltonian is non-zero only if the system has energy. So in both cases above, I would expect the wave function to be changing in time.
Also, the broader the wave function, the narrower the momentum function -which measures the distribution of momentum through space-. In the case of the electrons in a wire, I guess they are constantly being atracted by the other charges that form the atoms and by the other electrons as well, but I don't have an idea of how fast they move (in average, at least). For a free electron, it would be easy to conclude that how fast the electron is moving will dictate how broader is its wave function.

I used the term wave function to mean position function, actually.
 
Physics news on Phys.org
  • #2
davidge said:
What about the broadness of the wave function of conduction electrons in a wire?
The bands are the limits of "infinite" spread.

Every system has an energy.
davidge said:
For a free electron, it would be easy to conclude that how fast the electron is moving will dictate how broader is its wave function.
The overall speed of the electron does not matter. You can always change to a frame where its (expectation value of) momentum is zero.
 
  • #3
mfb said:
You can always change to a frame where its (expectation value of) momentum is zero.
So that means that the very existence of a particle is dependent on the frame? Because we can change to a frame where its wave function has a different value at a same position in space.
 
  • #4
davidge said:
So that means that the very existence of a particle is dependent on the frame?
No. At least not in this context.
davidge said:
Because we can change to a frame where its wave function has a different value at a same position in space.
The wave function will look different for different observers, of course. That is not a result of quantum mechanics, you already have different properties in classical mechanics.
 
  • #5
Ok. So, returning to the point of the thread, what can we conclude about the wave function for electrons in a current and for a free electron?
 
  • #6
davidge said:
Ok. So, returning to the point of the thread, what can we conclude about the wave function for electrons in a current and for a free electron?
You can conclude that any differences between the two are frame-dependent.
 
  • #7
Nugatory said:
You can conclude that any differences between the two are frame-dependent.
but certainly there are other important differences
 

1. What is the distribution of a particle in a uniform electric field?

The distribution of a particle in a uniform electric field is characterized by a constant acceleration in the direction of the field. This means that the particle will move in a straight line with a constant velocity. The distribution of the particle's position will be linear and its speed will increase over time.

2. How does the distribution of a particle change in a non-uniform electric field?

In a non-uniform electric field, the distribution of a particle will be affected by the varying strength and direction of the field. This can cause the particle to experience a changing acceleration, resulting in a curved path and a non-linear distribution of its position. The particle's speed may also vary as it moves through the field.

3. What is the Maxwell-Boltzmann distribution and how does it relate to particles in a gas?

The Maxwell-Boltzmann distribution is a probability distribution that describes the distribution of speeds for particles in a gas at a given temperature. It shows that the majority of particles have speeds close to the average, with fewer particles having higher or lower speeds. This distribution is important in understanding the behavior of gases and their physical properties.

4. How does the distribution of particles change in a liquid or solid state compared to a gas?

In a liquid or solid state, particles are much closer together and have stronger intermolecular forces than in a gas. This results in a more ordered and structured distribution of particles, with less random motion and a lower average speed compared to particles in a gas. In a solid, particles are arranged in a specific lattice structure, while in a liquid they are able to move and flow but still maintain close proximity to one another.

5. Can the distribution of a particle be affected by external factors, such as external forces or collisions?

Yes, the distribution of a particle can be influenced by external factors such as external forces or collisions with other particles. These external factors can change the particle's speed, direction, and position, resulting in a different distribution than what would be expected in a vacuum. For example, collisions with other particles can cause a particle to deviate from its expected path and result in a non-uniform distribution of its position.

Similar threads

I Measurement problem - will this work?
    • Quantum Physics
Replies
3
Views
247
I "Wave-particle duality" and double-slit experiment
    • Quantum Physics
2
Replies
36
Views
1K
I Free particle probability distribution
    • Quantum Physics
Replies
22
Views
937
I Exploring Microscopic Particles: Interactions & Measurement
    • Quantum Physics
Replies
4
Views
854
I Non-wave solution to wave equation and virtual particles
    • Quantum Physics
Replies
9
Views
772
I Understanding Wave Function Probabilities for a Free Particle
    • Quantum Physics
Replies
25
Views
1K
B Wave-particle duality of atoms and molecules
    • Quantum Physics
2
Replies
38
Views
2K
B Extremely elementary questions about QM
    • Quantum Physics
Replies
24
Views
1K
I Splitting of a one-particle wave function
    • Quantum Physics
Replies
15
Views
1K
A Does the quantum space of states have countable or uncountable basis?
    • Quantum Physics
2
Replies
67
Views
5K

Hot Threads

Recent Insights

Back
Top