Quantum Mechanics Proof Homework Help

Click For Summary

Homework Help Overview

The discussion revolves around proving that the function u(z,t)=f(z-vt) satisfies the wave equation ∂²u/∂t² = v² · ∂²u/∂z². The subject area is quantum mechanics, specifically focusing on wave equations.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to relate the problem to Lorentz law but expresses difficulty in making progress. Another participant questions the relevance of Lorentz law and prompts the original poster to consider how to take the partial time-derivative of the function f(z-vt).

Discussion Status

The discussion is ongoing, with participants providing guidance on the necessary mathematical approach and questioning the assumptions made by the original poster. There is no explicit consensus yet, as the original poster has not yet provided a detailed attempt at a solution.

Contextual Notes

Participants note the importance of following forum guidelines, which include demonstrating effort in the problem-solving process and using the appropriate template for posting.

SlushmanIU
Messages
2
Reaction score
0
I was asked to prove that any function u(z,t)=f(z-vt) is a solution of the wave equation
∂2u/ dt2= v2 · ∂2u/dz2

I know that v is constant and z and t are independent. I've tried looking at Lorentz law but I am getting nowhere fast. Please help!
 
Physics news on Phys.org
Hello Slushman, and welcome to the wonderful world of PF :)

We don't have many rules (just a bunch of well-meant guidelines, which please read). They do require (so you could construe that as a rule) some effort on your part in the sense that you show your attempt at solution. They also want you (so you could construe that as a rule as well -- but it's all well meant!) to use the template, which happened to disappear as if by magic from your post. Pity, I could have helped immediately, instead of tomorrow morning (it's late here, but perhaps others ...)

1. Homework Statement

2. Homework Equations

3. The Attempt at a Solution

When I fill in the propposed solution, I get ...​
 
Hi. This is pure mathematics so Lorentz has nothing to do with your proof:
How do you take the partial time-derivative of f(z-vt)? That is: f[z(t) -vt]?
Look up a calculus book if that's unfamiliar..
 
Slushman still there ?
 

Similar threads

  • · Replies 27 ·
Replies
27
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 47 ·
2
Replies
47
Views
4K
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 7 ·
Replies
7
Views
1K
  • · Replies 16 ·
Replies
16
Views
1K