(a) Show that $\left[\hat{A},\left[\hat{B},\hat{C}\right]\right]+\left[\hat{B},\left[\hat{C},\hat{A}\right]\right]+\left[\hat{C},\left[\hat{A},\hat{B}\right]\right]=0$ (b) Calculate the commutator value of $L^2$ and $L_z$ i.e., $\left[\hat{L^2},\hat{L_z}\right]$ Where $L^2 = L_x^2 + L_y^2 + L_z^2$
Added by Francisco Jose W.
Close
Step 1
(a) To prove the given equation, we need to show that the sum of the three terms on the left-hand side equals zero. Show more…
Show all steps
Your feedback will help us improve your experience
Mukesh Devi and 89 other Physics 103 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
(a) Using [X, P] = ih, show that [X^2, P] = 2ihX and [X, P^2] = 2ihP. (b) Show that [X^2, P^2] = 2ih(ih + 2PX). (c) Calculate the commutator [X^2, P^3].
Adi S.
(a) Prove the following commutator identity: $$ [A B, C]=A[B \cdot C]+[A \cdot C] B $$ (b) Show that $$ \left[x^{n} \cdot p\right]=i \hbar n x^{n-1} . $$ (c) Show more generally that $$ [f(x), p]=i \hbar \frac{d f}{d x} $$ for any function $f(x)$.
Formalism
The Uncertainty Principle
prove the following commutator relation: [A,[B,C]]+[B,[C,A]]+[C,[A,B]]=0 jacobi Identity
Supreeta N.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD