Easy way to get the expectation value of momentum squared?

Click For Summary
SUMMARY

The discussion centers on the relationship between momentum squared () and position squared () in the context of Gaussian distributions. The user seeks to express in terms of to simplify calculations. It is established that to obtain , one must apply the position-space operator twice. Additionally, the conversation touches on the classical relationship between

^2 and , indicating a deeper exploration of these concepts is necessary.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically momentum and position operators.
  • Familiarity with Gaussian distributions and their properties.
  • Knowledge of classical mechanics, particularly the relationships between momentum and position.
  • Basic mathematical skills for manipulating operators and equations.
NEXT STEPS
  • Research the application of position-space operators in quantum mechanics.
  • Study the mathematical properties of Gaussian distributions in physics.
  • Explore the classical and quantum relationships between momentum and position.
  • Learn about operator algebra in quantum mechanics for better manipulation of and .
USEFUL FOR

Students and professionals in physics, particularly those focused on quantum mechanics and mathematical physics, will benefit from this discussion.

chi-young
Messages
9
Reaction score
0
Hello, I've been trying to define <p2> in terms of <x2>, much the same way that you can write <p> = m d<x>/dt, because it would be easier in my calculations.

Is this possible, or am I on a fools errand?

Edit: For Gaussian distributions.
 
Physics news on Phys.org
To get p^2 you apply the position-space operator twice.
What's the problem?

Oh you want the classical relation - so you'd need the relationship between <p>^2 and <p^2>?
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
View full post »

Similar threads

Undergrad Expectation value of the momentum for an electron in a box
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad Other ways of finding expectation value of momentum
  • · Replies 8 ·
Replies
8
Views
2K
High School A stupidly basic question about expectation value
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Mean values of observables
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Expectation value of momentum for free particle
  • · Replies 8 ·
Replies
8
Views
6K
Undergrad Expectation value of energy in TISE
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Hermitian and expectation values.... imaginary?
  • · Replies 20 ·
Replies
20
Views
4K
Calculating Expectation Value of Momentum with Fourier Transform
  • · Replies 2 ·
Replies
2
Views
2K
Question about expectation values.
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad 1D wavepacket scattering simulation, momentum distribution formula
  • · Replies 24 ·
Replies
24
Views
2K