Sinusoidal Potential in Schroedinger

  • Context: Undergrad 
  • Thread starter Thread starter Sturk200
  • Start date Start date
  • Tags Tags
    Potential Sinusoidal
Click For Summary
SUMMARY

The discussion centers on solving the time-independent Schrödinger equation for a sinusoidal potential defined as V=sin(x). Participants confirm that Bloch's theorem is applicable due to the periodic nature of the potential, allowing for the derivation of wave functions. Additionally, a series approximation for sin(x) can be utilized to obtain a series solution for the wave function, psi. A reference to a relevant publication is provided for further reading on the topic.

PREREQUISITES
  • Understanding of Schrödinger's equation
  • Familiarity with Bloch's theorem
  • Knowledge of periodic potentials in quantum mechanics
  • Basic concepts of wave functions and their solutions
NEXT STEPS
  • Study the application of Bloch's theorem in periodic potentials
  • Explore series solutions for wave functions in quantum mechanics
  • Review the publication linked in the discussion for advanced insights
  • Investigate the implications of sinusoidal potentials on quantum states
USEFUL FOR

Quantum physicists, students of quantum mechanics, and researchers interested in periodic potentials and their effects on wave functions.

Sturk200
Messages
168
Reaction score
17
Hello,

How do you solve Schroedinger's equation (time-independent, in one dimension) if the potential is V=sin(x)? Do you have to use the series approximation for sin(x) and obtain a series solution for psi? Is there some way to use Bloch's theorem since the potential is periodic? I've only seen Bloch used for a periodic delta function potential. Does anybody know what these wave functions look like?

Thanks!
 
Physics news on Phys.org
Sturk200 said:
Is there some way to use Bloch's theorem since the potential is periodic?
Bloch theorem should be usable as it is derived for general periodic potentials. Reference wise, I think you might want to look at https://vcq.quantum.at/fileadmin/Publications/1999-12.pdf.
 

Similar threads

Graduate Dimension of \lambda constant in \delta potential
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Can Bloch Waves Reveal Periodic Potentials in Quantum Mechanics?
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Understanding Bloch's Theorem: Does 'n' Label Energy Bands?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad I would like an explanation of these extra energy states
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Completeness of Eigenfunctions of Hermitian Operators
  • · Replies 22 ·
Replies
22
Views
3K
Undergrad Mathematical basics of quantum mechanics
  • · Replies 21 ·
Replies
21
Views
3K
Undergrad When does an even potential give both even and odd solutions to Schrodinger's Eqn?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Scattering Theory: Difference between use of scattering amplitude and Born approximation?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Bound states of a periodic potential well in one dimension
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Periodic potential - energy bands
  • · Replies 8 ·
Replies
8
Views
2K