Proving Parity in Normalized Solutions of the Schrodinger Equation

  • Thread starter Thread starter ProfessorChaos
  • Start date Start date
  • Tags Tags
    Proof Schrödinger
AI Thread Summary
The discussion focuses on demonstrating that normalized solutions to the time-independent Schrödinger equation exhibit definite parity when the potential V(x) is even, meaning V(x) = V(-x). The user is struggling to prove that the solutions satisfy the condition u(x) = ±u(-x). They attempted to substitute y = -x into the equation but found their approach unconvincing and did not achieve a clear solution. The user seeks guidance on how to effectively normalize their findings and establish the parity of the solutions. Overall, the thread highlights the challenge of proving parity in quantum mechanics under specific potential conditions.
ProfessorChaos
Messages
2
Reaction score
0
Hopefully this is in the correct section.

Struggling with this question though I don't think it should be particularly difficult:

Show that if V(x) = V(-x) normalised solutions to the time-independent Schrodinger equation have definite parity - that is, u(x) = +-u(-x)

(+- means plus or minus. Sorry for poor formatting - on phone)

Thanks in advance.
 
Physics news on Phys.org
Just read the "how to ask for help" sticky.

My attempt at a solution involved subbing y = -x. Obtaining a solution, then trying to normalise it. However I don't get anywhere really, and my line of argument through my current page of working reads unconvincing (I'm just guessing).

Cheers
 
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »

Similar threads

Prove that ##\psi## is a solution to Schrödinger equation
Replies
9
Views
2K
Time Independent Schrodinger Equation
Replies
1
Views
1K
Schrodinger Equation/verify solution
Replies
2
Views
2K
I Derivation of Schrodinger equation (chicken and egg problem?)
Replies
17
Views
3K
How to normalize Schrodinger equation
Replies
5
Views
5K
Proof of Schrodinger equation solution persisting in time
Replies
5
Views
1K
Non trivial solution to Schrödinger equation for 1-D infinite well
Replies
3
Views
2K
1 Dimentional Schrodinger equation
Replies
1
Views
2K
Solutions to schrodinger equation with potential V(x)=V(-x)
Replies
4
Views
2K
I Novel Schrodinger equation examples for 1D
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top