# Acceleration. Infinite potential well.

• LagrangeEuler
In summary: in a potential well, the particle could theoretically gain or lose energy in a continuous way, as long as its position remained invariant.
LagrangeEuler
Why we don't have acceleration in quantum mechanics. For example why particle in infinite potential well can not accelerate. For example dimension of well is ##L## and ##L=\frac{at^2}{2}##, where ##a## is acceleration.

LagrangeEuler said:
For example dimension of well is ##L## and ##L=\frac{at^2}{2}##, where ##a## is acceleration.

What's your reasoning here? In the usual infinite square well, the potential is constant (zero) inside the well. Classically, the force on the particle would be zero everywhere except at the walls, like a molecule in an ideal gas. The particle's acceleration would also be zero at all times except when it's colliding with one of the walls.

More important, in order to talk about the acceleration of a particle, it has to have a trajectory: a well-defined position as a function of t. In QM we don't have that, except in the Bohmian interpretation where the trajectories are highly non-classical anyway.

Additionally, it would be weird to talk about acceleration for any system which has discrete energy states... acceleration would mean that the particle would gain/lose energy in some continuous amounts, and that would need it to change its energy respectively...
In the same way someone would say that the electron accelerating inside the atom, would have to radiate its energy and "fall" into the nucleus...

Of course I believe fundamentally the reason is what jtbell stated in #2

Well I define in potential well that ##\langle p \rangle=0##. Could I interprete this like particle goes from left to right as much as it goes from right to left in the well. So I can say that impulse in one direction is ##p##, and in the other is ##-p## so ##\langle p \rangle=0##. Why the particle does not loose some energy in contact with the walls.

because the walls are very strong...
If you had a finite well potential, there would be penetration/transition...

Yes you can, interpret it like that. But that's only because the mean values behave like classical quantities...

## 1. What is an "infinite potential well" in the context of acceleration?

An infinite potential well is a theoretical concept in quantum mechanics that represents a confined space with infinitely high potential barriers. This serves as a model for studying the behavior of a particle trapped in a specific region, where its energy is limited and the potential remains constant.

## 2. How does acceleration occur in an infinite potential well?

In an infinite potential well, the particle is confined within a specific region and cannot escape due to the infinitely high potential barriers. However, the particle can still experience acceleration within this confined space as its energy and position change over time.

## 3. What is the relationship between acceleration and wave properties in an infinite potential well?

In an infinite potential well, the particle is described by a standing wave function that represents its probability of existence at different points within the well. The acceleration of the particle is related to the gradient of this wave function, which is responsible for the changing energy and position of the particle over time.

## 4. Can the acceleration of a particle in an infinite potential well be predicted?

Yes, the acceleration of a particle in an infinite potential well can be predicted using the Schrödinger equation. This equation takes into account the potential barriers and the wave function of the particle to determine its acceleration at any given point in time.

## 5. How does the concept of "tunneling" relate to acceleration in an infinite potential well?

In quantum mechanics, "tunneling" refers to the phenomenon where a particle can pass through a potential barrier, even if it does not have enough energy to overcome it. In an infinite potential well, the acceleration of a particle can lead to tunneling, as the changing energy and position of the particle can enable it to pass through the infinitely high potential barriers.

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