Register to reply

Quantum - Electron in an infinite rectangular prism well

by golmschenk
Tags: electron, infinite, prism, quantum, rectangular
Share this thread:
golmschenk
#1
Nov16-09, 11:47 PM
P: 36
1. The problem statement, all variables and given/known data
If an electron is in an infinite rectangular prism well, with sides of length a, b, and c where c is the shortest and (b^2)*c=a^3, for what value of the d=b/c is the first excited state of the electron minimized? This isn't the complete problem but it's the part that's giving me trouble/

2. Relevant equations
I'm using the equations E=(h^2*pi^2/(2m))*((n_x/l_x)^2*(n_y/l_y)^2*(n_z/l_z)^2) but it's suppose to be used for an electron gas in a solid. The question is referring to a crystal. Is this equation one I want to use? Sorry for not using the correct math notation to make it look nice.

3. The attempt at a solution
My attempted solution is basically just plugging it into that equation.

Thanks for your time.
Phys.Org News Partner Science news on Phys.org
Scientists develop 'electronic nose' for rapid detection of C. diff infection
Why plants in the office make us more productive
Tesla Motors dealing as states play factory poker
lanedance
#2
Nov18-09, 02:22 AM
HW Helper
P: 3,307
Quote Quote by golmschenk View Post
1. The problem statement, all variables and given/known data
If an electron is in an infinite rectangular prism well, with sides of length a, b, and c where c is the shortest and (b^2)*c=a^3, for what value of the d=b/c is the first excited state of the electron minimized? This isn't the complete problem but it's the part that's giving me trouble/

2. Relevant equations
I'm using the equations E=(h^2*pi^2/(2m))*((n_x/l_x)^2*(n_y/l_y)^2*(n_z/l_z)^2) but it's suppose to be used for an electron gas in a solid. The question is referring to a crystal. Is this equation one I want to use? Sorry for not using the correct math notation to make it look nice.

Thanks for your time.
i'm not that familiar with the equation you give, but don't think its the the correct one to use

the infinite potential rectangular box has a reasonable analytic solution solved through separation of variables (the spatial cartesian variables can be separated in the DE )

you will get a similar equation to the one you quote for energy, however the [itex] \frac({n_x}{L_x})^2[/itex] terms are summed not multiplied
golmschenk
#3
Nov18-09, 07:14 PM
P: 36
Oops, yeah, summed is actually what I meant to type. And I think that ended up working out. I don't know for sure that I got the right answer yet, but it seemed to work. Thanks.


Register to reply

Related Discussions
Moving a rectangular prism through a magnetic field Introductory Physics Homework 0
Moment of inertia for rectangular prism General Engineering 2
Related Rates (rectangular prism) Calculus & Beyond Homework 4
Electromagnetism - Magnetic flux between infinite wire and rectangular loop Introductory Physics Homework 0
Quantum... rectangular barrier Advanced Physics Homework 4