Quantum Mechanics Operators question

zheng89120
Messages
139
Reaction score
0

Homework Statement



The operator Q obeys the commutation relation [Q, H] = EoQ, where Eo is a constant with units of energy. Show that if ψ(x) is a solution of the time-independent Schrodinger equation with energy E, then Qψ(x) is also a solution of the time-independent Schrodinger equation, and determine the energy corresponding to Qψ(x).

Homework Equations



Commutator calculation and properties

? Time-independent Schrodinger equation and solution

The Attempt at a Solution



QH-HQ = EoQ

Q = (QH-HQ)/Eo

Qψ = QC1eiA1/2x+QC2e-iA1/2x
 
Physics news on Phys.org
Your approach seems a little strange. ψ satisfies Hψ = Eψ (the time independent Schrodinger equation). Then write an expression for H(Qψ) by using the commutator you are given and the fact that Hψ = Eψ.
 

Thread 'Initial conditions for orbits around a wormhole'

Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
View full post »

Thread 'Help to convert units of a simple formula'

The value of H equals ## 10^{3}## in natural units, According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##, ## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units. So is this conversion correct? Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?
View full post »

Similar threads

Checking that a given potential has a ground state
Replies
4
Views
648
How Does Time Evolution Affect Quantum Measurement Probabilities?
Replies
7
Views
3K
Linear operators, quantum mechanics
Replies
12
Views
2K
Why Does [H, Q] = 0 Imply d<Q>/dt = 0?
Replies
1
Views
2K
I The postulate of Quantum Mechanics and Eigenvalue equation
Replies
5
Views
1K
Does this operator commute with the Hamiltonian operator?
Replies
1
Views
2K
What is the operator for kinetic energy in the Schrodinger equation?
Replies
1
Views
1K
Pauli Equation - Simple operator algebra question
Replies
3
Views
2K
Hamiltonians and Expectation Values and Ehrenfest's theorum, OH MY ()
Replies
1
Views
2K
Time Derivatives of Expectation Value of X^2 in a Harmonic Oscillator
Replies
2
Views
3K

Hot Threads

Recent Insights

Back
Top