Need help with particle in a box

In summary, when the width of the box is doubled, the particle has a 50% chance of remaining in the same state as before. If the width of the box is tripled, the particle has a 3% chance of remaining in the same state. If the width of the box is quadrupled, the particle has a 0.3% chance of remaining in the same state.
  • #1
TPDC130
6
0
Hi, I am new to these concepts and i need help on answering some assignment questions.

the question is:
a particle of mass m is confined in a 1-d box of width L in the third excited state.
a) suppose the width of the box is suddenly doubled. find the probability that the particle remains in the same state.
b) calculate the prob that the particle drops to ground state when size is doubled.
c) calculate the probability that the particle initially in ground state remains in round state when size of box is reduced to L/2

i have no idea where to start on this and any help would be great
 
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  • #2
This will be moved to the Home Work section.

Please show you attempt to solution, if you don't have any idea, make atl east a serious guess.

Also write down the equations and formulas that you are familiar with. (eg. what a square well is, etc)

Since you are new here, I am nice to you and will give you a hint, in the future - read and follow the rules.

Hint: start by solving the Shrodinger equation for a square well with length [itex] \nu L [/itex], where [itex] \nu = 1,2,3, ... [/itex]
 
  • #3
ok, I am sorry for not including much. i didnt realize. this is new to me as i said. anyway, i am able to solve and get the wavefunction which turns out to be psi(x)=Asin(kx). and if i did my calculations correct, i think the energy in the 3rd excited state is given by E=(16*pi^2*hbar^2)/(2*m*L). i know how to find the probability that's its in a certain part of the box i.e. between L/2 and 3L/4 for example. but i have no idea to find the probability that its in a certain state or the prob that its still in that state when the well size is increased
 
  • #4
You have two sets of eigenstates, one for L and one for 2L. Can you expand one set of eigenstates in terms of the other? If so, why would you want to do so?
Good luck
Reilly Atkinson
 

What is a particle in a box?

A particle in a box is a simplified model used in quantum mechanics to study the behavior of a particle confined to a one-dimensional space. The particle is assumed to be confined within an infinitely high potential energy barrier, creating a "box" or finite region where the particle can exist.

What is the significance of studying particles in a box?

Studying particles in a box allows scientists to understand the fundamental principles of quantum mechanics, such as wave-particle duality and the quantization of energy levels. It also serves as a useful tool for understanding more complex systems, such as atoms and molecules.

What are the boundary conditions for a particle in a box?

The boundary conditions for a particle in a box are that the wave function must be continuous and differentiable at the boundaries of the box. This means that the wave function must approach zero at the boundaries, representing the particle being confined within the box.

How do you solve for the energy levels of a particle in a box?

The energy levels of a particle in a box can be solved using the Schrödinger equation and applying the boundary conditions. The energy levels are quantized, meaning they can only take on specific, discrete values.

What are some real-world applications of studying particles in a box?

Studying particles in a box has applications in various fields, including solid-state physics, materials science, and nanotechnology. It can also help in understanding the behavior of electrons in semiconductor devices, which are essential for modern technology.

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