Eigenvalue Question (p2.14 in Quantum Chemistry and Spectroscopy)

Click For Summary
SUMMARY

The discussion centers on the eigenvalue problem involving the function e^(-x^2/2) and the operator d^2/dx^2 - x^2. The consensus is that e^(-x^2/2) is indeed an eigenfunction of the operator, yielding an eigenvalue of -6, as stated in the answer key. However, there is confusion regarding the derivative calculations, particularly with Wolfram Alpha's output, which suggests an alternative interpretation. The operator x + d/dx is also mentioned, indicating a need for clarity on how to determine its eigenvalue.

PREREQUISITES
  • Understanding of eigenvalues and eigenfunctions in quantum mechanics.
  • Familiarity with differential operators, specifically d^2/dx^2.
  • Knowledge of Gaussian functions and their properties.
  • Basic proficiency in using computational tools like Wolfram Alpha for verification.
NEXT STEPS
  • Study the derivation of eigenvalues for the operator d^2/dx^2 - x^2 in quantum mechanics.
  • Learn about the properties of Gaussian functions and their role in quantum mechanics.
  • Explore the application of the operator x + d/dx in eigenvalue problems.
  • Review the use of computational tools for solving differential equations and verifying eigenvalue calculations.
USEFUL FOR

Students and professionals in quantum chemistry, physicists dealing with quantum mechanics, and anyone interested in understanding eigenvalue problems related to differential operators.

anduril66
Messages
1
Reaction score
0
function: e^-(x^2/2)
operator: d^2/dx^2 -x^2

The answer key says the function is an eigenfunction of the operator with an eigenvalue of -6.

I can't figure out how to reach this conclusion. Also, Wolfram Alpha says d/dx(d/(dx)e^(-x^2/2)) = e^(-x^2/2) (x^2-1). Isn't this inconsistent with the answer key? Thanks.
 
Physics news on Phys.org
It is an eigenfunction, but with different eigenvalue.

ehild
 
guys please help me doing this,
the operator is given as x+ d/dx
i have to find the eigenvalue. how to do it?
 

Similar threads

Correct Setup for Finite Difference to Calculate Quantum Tunneling
  • · Replies 2 ·
Replies
2
Views
1K
Quantum Mechanics I, finding impuls wavefunction.
  • · Replies 6 ·
Replies
6
Views
1K
Force between charged Ring and Rod, disproved Newtons 3rd law?
  • · Replies 3 ·
Replies
3
Views
2K
Help Calculating probability between 2 limits for the ground state
  • · Replies 28 ·
Replies
28
Views
2K
Understanding a math step in solving Schrödinger's equation for single particle in a box
  • · Replies 8 ·
Replies
8
Views
1K
Griffiths' Quantum Mechanics Problem 4.27 : Diatomic particles
  • · Replies 46 ·
2
Replies
46
Views
3K
Block sliding on vertical track with friction (Solved problem)
  • · Replies 4 ·
Replies
4
Views
3K
Graduate The eigenvalue power method for quantum problems
  • · Replies 2 ·
Replies
2
Views
2K
Show that the two wave functions are eigenfunction
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad More information on the momentum eigenstate in the position basis
  • · Replies 1 ·
Replies
1
Views
1K