# Quantum harmonic oscillators DE wavefunction

• moriheru
In summary, the conversation is about a simple differential equation for the zeroth wavefunction of a harmonic oscillator. The person asking the question has a solution but it differs by a constant and they are seeking clarification on their mistake. They provide the equation, which is missing a psi function, and mention that they will edit the Latex for it. They also specify that their solution is different from the one in the book and are asking for help in identifying their error.
moriheru
My question concerns a really simple differential equation for the zeroth wavefunction of a harmonic oscillator.
I have pretty much got it but my solution just differs by a constant,so I thought why think when one can ask other people :). Here is the equation:

Where the x star represent a variable involving mass frequency and Plancks constant. There is a psi function missing in the second equation (for any latex tips please e-mail me)
(Posted to early so there was no equation on the original post;had to edit it)

Last edited:
Sorry Latex is wrong change it in a minute. So here it is.

Last edited:
Is should specify: the above is my solution and my question is what I did wrong as my book has a different solution.
Thanks for any help.

## What is a quantum harmonic oscillator?

A quantum harmonic oscillator is a physical system that exhibits the properties of both classical and quantum mechanics. It consists of a particle bound to a potential well and oscillating back and forth with a specific frequency.

## What is the DE wavefunction for a quantum harmonic oscillator?

The DE wavefunction for a quantum harmonic oscillator is a mathematical representation of the probability distribution of the particle's position and momentum at any given time. It is described by the Schrödinger equation and takes the form of a Gaussian or bell-shaped curve.

## How does the DE wavefunction change over time?

The DE wavefunction evolves over time according to the Schrödinger equation, which takes into account the potential energy of the particle and its initial conditions. As time goes on, the wavefunction will spread out and become more spread out, representing a larger range of possible positions and momentums for the particle.

## What is the significance of the energy levels in a quantum harmonic oscillator?

The energy levels in a quantum harmonic oscillator correspond to the allowed energies of the particle within the potential well. These levels are quantized, meaning they can only take on discrete values and are dependent on the frequency of the oscillation. This plays a crucial role in understanding the behavior of the system and its interactions with other particles.

## How does the quantum harmonic oscillator relate to real-world applications?

The quantum harmonic oscillator has many real-world applications, particularly in physics and engineering. It is used to model systems such as atoms, molecules, and even electronic circuits. It also has important applications in quantum computing and in understanding the behavior of materials at a microscopic level.

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