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...
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You have a tool that works for you and you know it well. Life is about more than just learning technology for technologies sake.
I just finished a take home final in quantum mechanics. It was a bear. I think this weekend I will get back to playing my...
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...
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...
Homework Statement
An oscillator is in the ground state of H = H^0 + H^1 , where the time-independent perturbation H^1 is the linear potential (-fx). It at t = 0, H^1 is abruptly turned off, determine the probability that the system is in the nth state of H^0 .
Homework...
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...
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...
Homework Statement
Particle described by wavefunction psi(r,theta,phi) = A*Exp[-r/a0] (a0 = constant)
(1) What is the angular momentum content of the state
(2) Assuming psi is an eigenstate in a potential that vanishes as r -> infinity, find E (match leading terms in Schrodinger's...
Thanks for the replies.
I believe Pete is correct. The constraining forces are not conservative and therefore are not associated with a potential in the Lagrangian. Constraining forces can be added to the Euler-Lagrange equation as Lagrange multipliers.
jsc
Problem: Consider a particle of mass m, constrained to move in a circle of radius r. Find the Lagrangian:
Relevant Equations: L = T - V
Where L is the Lagrangian, T is the kinetic energy, and V is the potential energy.
My questions is this. T is the kinetic energy and would simply...
Matlab is good for numerical calculations. Matlab commands are easier to learn and its expressions are less cryptic than Mathematica. You can save sequences of commands and build functions using .m files. Matlab then allows you to run these .m files like you would run an interpreted program...