Ground state energy and wavefuntion?

In summary, the conversation discusses finding the ground state energy and wavefunction for a particle of mass m moving in a potential that is infinite at x<0 and V=(1/2)mw^2x^2 at x>0. The person asking the question is struggling with finding a solution due to the infinite potential on one side, but is reminded of the quantum simple harmonic oscillator and will attempt to solve using that concept.
  • #1
pbeary
4
0

Homework Statement


Find the ground state energy and the ground state wavefunction for a particle of mass m moving in the potential

V=[itex]\frac{1}{2}[/itex]mw[itex]^{2}[/itex]x[itex]^{2}[/itex] at x>0
V=[itex]\infty[/itex] at x<0


The Attempt at a Solution



Well, the problem I am having is that I have answering questions that always had a boundary such as -a<x<a or something of the like, but now that only one side looks like an infinite potential well, I am confused towards how I should tackle this problem...

can someone give me a hint so I can at least try to solve this?
thanks!
 
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  • #2
Are you already familiar with the quantum simple harmonic oscillator?
 
  • #3
Oh! yes, I see now :)
I was too focused on simple wells that I forgot about it completely!
I'll give it a go and see how I do.

Thanks.
 

FAQ: Ground state energy and wavefuntion?

1. What is ground state energy?

Ground state energy refers to the minimum amount of energy that a system can have. It is the energy of the lowest possible energy level that an electron can occupy in an atom or molecule.

2. How is ground state energy calculated?

Ground state energy is calculated using the Schrödinger equation, which is a mathematical equation that describes the behavior of quantum particles, such as electrons. This equation takes into account factors such as the mass and charge of the particle, as well as the potential energy of the system.

3. What is a wave function?

A wave function is a mathematical representation of the quantum state of a particle. It describes the probability of finding a particle in a certain position or state, and it is used to calculate properties such as energy and momentum.

4. How does the wave function relate to ground state energy?

The wave function is directly related to the ground state energy of a system. The lowest energy level of a particle is represented by the lowest energy state of the wave function, and the shape of the wave function can provide information about the distribution of the particle's energy.

5. Can ground state energy be changed?

In quantum mechanics, ground state energy is considered to be the lowest possible energy level. However, it is possible for a particle to gain or lose energy and move to a higher or lower energy state. This can happen through interactions with other particles or by applying an external energy source.

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