Show that [x2, px2] = 2ih(xpx +p xx)
We need to evaluate the commutator: \[ [x^2, p_x x^2] \] and show that it simplifies to: \[ [x^2, p_x x^2] = 2i\hbar (x p_x + p_x x). \] ### Step 1: Expand the Commutator Using the definition of the commutator \([A, B] = AB - BA\), we expand: \[ [x^2, p_x x^2] = x^2 (p_x x^2) - (p_x x^2) x^2. ____ _______ __________ __________ ___ ______ _________ _______ _____.
______ ____ ________ ___ __________ ________ ________ ___ _____ _____.
_________ ____ ____ __________ _________ ___ _________ ____ ________ ______ ___.
______ ____ _______ ________ _____ _____ _____ _____ _________ _________ ______ _____.
____ ____ ______ __________ _____ ________ _________ ___.
___ ______ ________ ______ ______ ______.
______ _____ ____ ________ ____ ____ ____ ____ ____ ______ __________ __________.
_________ _________ ______ _______ ____ ________.
________ ___ _____ ________ ___ ___ _________ ________ _________.
___ _______ ____ _________ _____ ___ __________ ___.
________ _________ __________ _______ __________ _____ _______.
_________ ___ ___ __________ _________ __________ _____ ____ __________ ____ _______ ____.
__________ ___ ______ __________ _______ _______ ____ _____.
______ _________ __________ ______ _________ ______ _____ ________ ________ ___.
_______ ___ _________ _______ _____ ________ ___ ______.
_________ ____ ___ _____ ______ _______ __________ _______ ____ _________ ____.
___ ______ _______ ___ ____.
___ _______ _____ _______ _____ ________.
_______ _____ ___ ________ __________ ___ ______ ___ _______ ______ __________.
_______ ____ _________ ________ _________ ________ ________ __________.
______ _________ _______ ________ _________ _________ _______.
Get Full Answer on WhatsApp
Calculate the probability that a simple harmonic oscillator in its ground state will be found beyond the classical turning points.
A two state system has the orthonormal energy eigenkets IE₁) and IE2) with eigenvalues E₁ and E2. If the initial state of the system is given by
, determine 
.
Show that [x2, px2] = 2ih(xpx +p xx)
i) Show that the Hamiltonian for a simple harmonic oscillator can be written in terms of the raising and lowering operators as Ĥ =
ii) Obtain the value of * (n|p-2|n) for the eigenket | n) of t of the simple harmonic oscillator.
i) Write down the angular momentum states |j,mj) for j = 2 and the eigenvalue of J2 and J₂ for each of these states.
ii) Determine J+ 2,1) and J_|2,1).
Consider an electron in the state
where 
, are the Hydrogen atom eigenfunctions. Determine the normalization constant N and the expectation values of the energy, L2 and Lz.
Derive the Heisenberg equations of motion for the simple harmonic oscillator.