What does show solutions to the schroedinger eqn mean?

  • Context: Graduate 
  • Thread starter Thread starter Kovalainen
  • Start date Start date
  • Tags Tags
    Mean
Click For Summary
SUMMARY

The discussion centers on demonstrating that a given wave function Ψ is a solution to the Schrödinger equation at later times. Participants confirm that the process involves substituting the time-dependent wave function into the equation to verify that the left-hand side (LHS) equals the right-hand side (RHS). Additionally, it is emphasized that identifying negligible components of Ψ for large time (t) is crucial for accurate analysis. The consensus is that a systematic approach of writing down the initial state and ensuring the equation holds identically is essential.

PREREQUISITES
  • Understanding of the Schrödinger equation
  • Familiarity with wave functions in quantum mechanics
  • Knowledge of time-dependent solutions in quantum systems
  • Basic calculus for manipulating equations
NEXT STEPS
  • Study the derivation of the time-dependent Schrödinger equation
  • Learn about wave function normalization and its implications
  • Explore the concept of negligible terms in asymptotic analysis
  • Investigate examples of specific wave functions and their solutions
USEFUL FOR

Students of quantum mechanics, particularly those studying wave functions and the Schrödinger equation, as well as educators looking for clear explanations of these concepts.

Kovalainen
Messages
1
Reaction score
0
What does "show solutions to the schroedinger eqn" mean?

I'm sorry for the very beginner question, I'm a mature student who's just come back to University so I'm unaccustomed to the terminology.

The question has given us a wave function and asked us to show that at later times Ψ is a solution to the schroedinger equation.

Is all I need to do plug it in and show that LHS = RHS?
 
Physics news on Phys.org


If they ask specifically for \psi at later times then I'm guessing you may want to find the parts of \psi that become negligible for large t. Then plugging in it should work.
 


You're right. Write down the initial state, and then the time-dependent wave function, plug it into the Schrödinger Equation, it make sure it holds identically.
 

Similar threads

Undergrad What does ## \psi^{*}\hat{H}\psi ## mean?
  • · Replies 9 ·
Replies
9
Views
4K
Graduate What does "solving a quantum mechanics problem" mean?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad What does motion mean in quantum mechanics?
  • · Replies 27 ·
Replies
27
Views
3K
Graduate What does this article mean? (The holographic principle and M-cosmology)
  • · Replies 1 ·
Replies
1
Views
2K
Graduate What is the meaning of this equation?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate QM Newbie: What Does 'Non-Degenerate Spectrum of Boundstates' Mean?
  • · Replies 2 ·
Replies
2
Views
2K
High School Extremely elementary questions about QM
  • · Replies 24 ·
Replies
24
Views
3K
Undergrad What does it mean -- polarization of a single photon?
  • · Replies 22 ·
Replies
22
Views
5K
High School QFT & QM Questions (about time, locality, gravity, etc.)
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Physical interpretation of phase in solutions to Schrodinger's Eqn?
  • · Replies 12 ·
Replies
12
Views
5K