Quantized energy in infinite potential well

1. Sep 14, 2009

rozan977

How does energy become quantized in an infinite potential well??

2. Sep 14, 2009

alxm

How do the harmonics of a finite string become quantized?

3. Sep 14, 2009

Feldoh

Honestly from a mathematical standpoint it comes about due to the boundary conditions of the Schrodinger equation for an infinite potential well.

4. Sep 14, 2009

Bob_for_short

The proper functions (eigenfunctions) of the Hamiltonian are sin(πnz) where z is the dimensionless length z=x/L. The proper values (eigenvalues) are proportional to (πn)2.

Any, I repeat, any wave inside the well can be decomposed in a sum of proper waves with some amplitudes. In general case the wave energy is not certain but dispersed. Only in the eigenstates the energy is certain.

5. Sep 14, 2009

Halcyon-on

As the frequencies of a string in a guitar $$E_n = h v_n = n h v$$

6. Sep 14, 2009

Halcyon-on

That is through (periodic) boundary conditions.

7. Sep 14, 2009

Halcyon-on

For this aspect, Pythagoras was the first to study a problem of QM mechanics.

http://img523.imageshack.us/img523/5874/pitagoradagafuriotheorixk5.jpg [Broken]

Last edited by a moderator: May 4, 2017
8. Sep 14, 2009

rozan977

But what if the solution we assume of Schrodinger equation be in exponential form??

9. Sep 15, 2009

Halcyon-on

it is completely equivalent.

10. Sep 15, 2009

Bob_for_short

In order to satisfy the boundary conditions the two complex exponentials have to have certain coefficients that make their sum to be sin(pi*n*x/L).

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook