GREPhysics.NET
GR | # Login | Register
   
  GR9277 #52
Problem
GREPhysics.NET Official Solution    Alternate Solutions
\prob{52}
A particle of mass m is confined to an infinitely deep square-well potential:
<br />
 V(x)&=&\infty,\;\;x\leq0,x\geq a \\<br />
 V(x)&=&0,\;\;0\lt x \lt a<br />

The normalized eigenfunctions, labeled by the quantum number n, are $\psi_n=\sqrt{\frac{2}{a}}\sin \frac{n\pi x}{a}$

The eigenfunctions satisfy the condition $\int_0^a \psi_n^*(x)\psi_l(x)dx=\delta_{nl},\delta_{nl}=1$ if $n=l$, otherwise $\delta_{nl}=0$. This is a statement that the eigenfunctions are


  1. solutions to the Schrodinger equation
  2. orthonormal
  3. bounded
  4. linearly dependent
  5. symmetric

Quantum Mechanics}Orthonormality

\langle \psi_m | \psi_n \rangle = \delta_{nm}

This is the definition of orthonormality, i.e., something that is both orthogonal (self dot others = 0) and normal (self dot self = 1).

See below for user comments and alternate solutions! See below for user comments and alternate solutions!
Alternate Solutions
There are no Alternate Solutions for this problem. Be the first to post one!
Comments
solarclathrate
2009-07-13 22:25:51
So, the answer is (B).NEC

Post A Comment!
You are replying to:
So, the answer is (B).

Username:
Password:
Click here to register.
This comment is best classified as a: (mouseover)
 
Mouseover the respective type above for an explanation of each type.

Bare Basic LaTeX Rosetta Stone

LaTeX syntax supported through dollar sign wrappers $, ex., $\alpha^2_0$ produces .
type this... to get...
$\int_0^\infty$
$\partial$
$\Rightarrow$
$\ddot{x},\dot{x}$
$\sqrt{z}$
$\langle my \rangle$
$\left( abacadabra \right)_{me}$
$\vec{E}$
$\frac{a}{b}$
 
The Sidebar Chatbox...
Scroll to see it, or resize your browser to ignore it...