Ehrenfest's theorem Definition and 19 Threads

Mine is a simple question, so I shall keep development at a minimum. If a particle is moving in the absence of a potential (##V(x) = 0##), then ##\frac{\langle\hat p \rangle}{dt} = \langle -\frac{\partial V}{\partial x}\rangle=0## will require that the momentum expectation value remains...

Homework Statement I have a general question how I calculate the expectation value of V (potential energy) with Ehrenfest’s theorem. Do I have to integrate d<p>/dt with respect to d<x>. Also if the potential is symmetric (even) would that mean the expectation value of the potential is 0...

This may seem rather silly, but how would I go about enunciating Ehrenfest’s theorem? Also, does anyone know what this theorem implies for the relation between classical and quantum mechanics? Any suggestions or help is greatly appreciated!

Homework Statement A particle of mass m and spin s, it's subject at next central potential: ## \begin{equation*} V(\mathbf{r})= \begin{cases} 0\text{ r<a}\\ V_0\text{ a<r<b}\\ 0\text{ r>b} \end{cases} \end{equation*} ## Find the constants of motion of the system and the set of...

While studying Ehrenfest's theorem I came across this formula for time-derivatives of expectation values. What I can't understand is why is position/momentum operator time-independent? What does it mean to be a time-dependent operator? Since position/momentum of a particle may change...

I know when the initial state (##\Psi(x,0)##) is given, ##\frac{d<x>}{dt} \not=<p>##. I thought you can only apply Ehrenfest's theorem when ##\Psi## is a function of x and t, however it seems like you can also apply it to the time-independent part (##\psi(x)##) by itself as well. Can someone...

Homework Statement Part (a): Derive Ehrenfest's Theorem. What is a good quantum number? Part (b): Write down the energy eigenvalues and sketch energy diagram showing first 6 levels. Part (c): What's the symmetry of the new system and what happens to energy levels? Find a new good quantum...

Homework Statement Show \frac{d}{dt}\langle\bf{L}\rangle = \langle \bf{N} \rangle where \bf{N} = \bf{r}\times(-\nabla V) 2. Homework Equations . \frac{d}{dt}\langle A \rangle = \frac{i}{\hbar} \langle [H, A] \rangle The Attempt at a Solution I get to this point...

Homework Statement Show that if H = -\gamma\mathbf{L\cdot B}, and B is position independent, \frac{\mathrm{d} \left \langle \mathbf{L} \right \rangle}{\mathrm{d} t}=\left \langle \boldsymbol\mu \times\mathbf{B} \right \rangle=\left \langle \boldsymbol\mu \right \rangle\times\mathbf{B} Here H...

I was looking at this proof of Ehrenfest's theorem http://farside.ph.utexas.edu/teaching/qmech/lectures/node35.html I'm confused about equation 158. It looks like the first term under the integral sign in the first expression is vanishing to obtain the second expression but I don't know why...

In proving the Ehrenfest Theorem This is the typical first line: \frac{d }{dt}<O> = \frac{\partial}{\partial t} <\psi|O|\psi> = <\dot{\psi}|O|\psi> + <\psi|O|\dot{\psi}>+<\psi|\dot{O}|\psi> My question is how can the exact differential \frac{d }{dt}<O> be changed the partial...

If I had a hamiltonian of the form iA(p + c), where A is a constant matrix, p the momentum operator and c an ordinary constant how do I find the time rate of change of the expectation momentum value? I've tried using Ehrenfest's theorem but I don't understand whether in [p,H], I should treat p...

Homework Statement Show that \frac{d<p>}{dt} = < - \frac{\partial V}{\partial x}> Homework Equations The Attempt at a Solution I am trying to repeat the derivation that griffiths gives for deriving <p>, but it doesn't seem to give me anything that would indicate this proof is correct. <p> =...

Is there any physical significance of this theorem? Can we make some kind of conclusion about space and time because the derivative of the expectation value of momentum with respect to time is equal to the negative of the expectation value of the derivative of potential energy w.r.t. space...

We have to apply Ehrenfest's theorem and I don't think it was ever explained well to us. I have read that expectation values of measurable quantities behave according to classical physics equations ie. M\frac{d\left<x(t)\right>}{dt} = \left<p(t)\right> I think I must be applying this idea...

Homework Statement Griffith's problem 1.12 Calculate d\left<p\right>/dt. Answer \frac{d\left<p\right>}{dt} = \left<\frac{dV}{dx}\right> 2. The attempt at a solution so we know that \left<p\right> = -i\hbar \int \left(\Psi^* \frac{d\Psi}{dx}\right) dx so then...

Hi, I'm trying to prove that for a particle in a potential V(r), the rate of change of the expectation value of the orbital angular momentum L is equal to the expectation value of the torque: \frac{d}{dt}<L> = <N> where N = r \times (-\bigtriangledown{V}) Basically, I'm having problems...

Can anyone tell me what is the Ehrenfest's Theorm in quantum mechanic, I don't understand how it can provide an example for correspondence principle?

I have been asked to "find a solution to Ehrenfest's Theorem" (in this case for the expectation value of position, of a particle confined to a circle). What does this mean - what kind of answer should i find?