Recent content by jsc314159

Correct, x' is a function of x and t in a coordinate system moving with the cart. However, in this coordinate system H is no longer an explicit function of t.

So in the case of the spring-mass on a cart moving with uniform velocity, which has time varying constraints, H can be represented as: H = \frac{p^2}{2m} + \frac{k}{2} (x - v_0t)^2 if the generalized coordinate is the position x of the mass. In this case H is the total energy...

So, if H is in a form H = T + V, H represents the total energy. However, if H is not in this form, like in the case of a charged particle moving in a magnetic field or in the case of time varying constraints, then H is not the total energy. Is this right? I suppose I am somewhat confused over...

I have a question on the Hamiltonian from a classical viewpoint. I understand that the Hamiltonian, H, is conserved if it has no explicit time dependence, in other words: \frac{\partial H}{\partial t} = 0 What I am not clear on is how one can determine whether a given Hamiltonian...

The Schrodinger equation is a form of the wave equation. It can be interpreted like a wave equation. The acceleration at each point on the wave function is due to the Hamiltonian and that the larger the concavity of the wavefunction at point, the larger the acceleration. Does that make...

I think the reason a_0 -> a_0/Z is because the Coulomb potential in the Hamiltonian changes from q^2/r to Zq^2/r . Is that right? jsc

Do you mean hydrogen with a nucleus of 1 proton and 3 neutrons? Tritium is a radioactive isotope of hydrogen with 1 proton and 2 neutrons. It usually decays via H^3 -> (He^3)^+ + e^- + \nu^- Perhaps H^4 would be unstable due to internuclear forces. jsc

Homework Statement Show that if we consider photoemission from the 1s state of a charge Z atom, \sigma \propto Z^5}} , in the limit p_fa_0/Z\hbar >> 1. Homework Equations \sigma = \frac{128a_0^3\pi e^2p_f^3}{3m\hbar^3\omegac[1+p_f^2a_0^2/\hbar^2]^4}} The Attempt at a Solution Actually...

Thanks nrged. That makes it clear.

Homework Statement In a beta decay H3 -> He3+, use the sudden perturbation approximation to determine the probability of that an electron initially in the 1s state of H3 will end up in the |n=16,l=3,m=0> state of He3+ Homework Equations |<n'l'm'|nlm>|^2 The Attempt at a Solution...

Sorry, I didn't know a thread already existed on this topic. I suppose that is what the search function for. jsc

Hello all. I only have a few posts here so I am somewhat new to the forum. I have been reading a number of the posts though and I am favorably impressed by many of the responses. I am also somewhat new to LaTex so please forgive my mistakes with it. I am interested in learning more about the...

The rabbit hole gets deeper. Besides x and p, t and E also have an associated uncertainty in QM. \Delta t * \Delta E \geq \hbar/2. From what I understand about this, it means that there is a finite limit on how well we can know the energy of a particle that has existed for a finite...

I will keep that in mind. Thanks again.

kdv, Thanks, that is the solution. How can I learn to see these types of things more effectively? jsc