# When is energy quantized in a one dimensional potential.

• ItsFootballNo
In summary: This is true for both classically allowed and forbidden regions, as the potential energy is still a function of position in both cases. In summary, the energy of a non relativistic particle moving in a 1D potential V(x) is quantized due to the quantization of both kinetic and potential energies.
ItsFootballNo

## Homework Statement

Consider a non relativistic particle moving in a 1D potential V(x). Do you consider the energy of a particle moving in this potential to be quantized?

## Homework Equations

V(x)=A exp{alpha^2 x^2}

## The Attempt at a Solution

I was a bit confused as I thought energy was always quantized. My other thought was whether it is merely quantized in classically allowed zones and not in classically forbidden regions. In this case, the classically forbidden zones would be when |x| is greater than sqrt{2E/mw^2} if we approximate the potential as a harmonic oscillator.

Thanks for any help and apologies for any stupid errors I might have made. :S

*I was also unsure whether this would come under advanced physics or intro physics and if I have posted in the wrong forum, I apologise.

Yes, the energy of a particle moving in a 1D potential V(x) is quantized. This is because the total energy of the particle, E, is equal to the sum of the kinetic energy, T, and potential energy, U: E=T+U. The kinetic energy of the particle is quantized according to the de Broglie equation, E=hf, where h is Planck's constant and f is the frequency of the particle's motion. The potential energy is also quantized, because it is a function of the position of the particle. Therefore, the total energy of the particle is quantized.

## 1. What is energy quantization?

Energy quantization refers to the concept that energy can only exist in discrete, specific values rather than being continuous. This means that energy levels are limited to certain values and cannot take on any value in between.

## 2. Why is energy quantized in a one dimensional potential?

Energy is quantized in a one dimensional potential because in this scenario, the energy of a particle is confined to a single dimension. This confinement leads to discrete energy levels, as the particle can only have certain amounts of energy due to its limited motion in one dimension.

## 3. How is energy quantization observed in one dimensional potentials?

Energy quantization in one dimensional potentials can be observed through experiments such as the particle in a box model or the quantum harmonic oscillator. In both of these scenarios, the energy levels of the particle are found to be discrete, supporting the concept of energy quantization.

## 4. What are the implications of energy quantization in one dimensional potentials?

The implications of energy quantization in one dimensional potentials are significant in understanding the behavior of particles at the quantum level. It helps explain phenomena such as the stability of atoms and the existence of discrete energy levels in atoms and molecules. It also plays a crucial role in technological advancements such as transistors and lasers.

## 5. Can energy be quantized in more than one dimension?

Yes, energy can be quantized in more than one dimension. In fact, in most real-life situations, particles are not confined to a single dimension, and thus energy quantization occurs in multiple dimensions. This is seen in the energy levels of atoms and molecules, which have both electronic and vibrational energy levels due to their confinement in three dimensions.

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