Hamiltonian Definition and 833 Threads

Why do operators representing some symmetry commute with the Hamiltonian?

I am working on a problem for homework and am supposed to show that the angular momentum operator squared commutes with H and that angular momentum and H also commute. This must be done in spherical coordinates and everything I see says "it's straightforward" but I don't see it. At least not...

Hi all, I'm trying to solve the 1D Schrodinger equation for an arbritary potential, to calculate Franck Condon factors for absorption and emmision spectra. I can do this using iterative techniques (e.g. the Numerov method), but I can't seem to get it to work by discretrizing the hamiltonian...

Q is a conserved charge if \{Q, H\} = 0 Show that q+\epsilon\delta q satisfies the equation of motion. \delta q = \{q, Q\} I couldn't find the proof. Anybody knows? My workings: \delta q = \{q, Q\} \delta\dot{q} = \{\{q,Q\},H\} = - \{\{Q,H\},q\} - \{\{H,q\},Q\} \delta\dot{q} = \{\{q,Q\},H\} =...

If we have the Einstein Lagrangian... L= \sqrt (-g)R my question is how do you get the Hamiltonian?..the approach by Wheeler-De Witt is to consider the line element: ds^2 = N(t)dt^^2 + g_ij dx^i dz^ j (Einstein sum convention) and then substitute it into the Lagrangian above and perform...

Hi, I have a question in a past exam paper which I can't quite understand how to prove. It reads: Give an expression for the Hamiltonian of the Helium atom. Neglecting the interaction between the electrons, derive the state function for the Helium ground state in terms of hydrogen-like...

defination of "eFz" in Hamiltonian I want to know the defination of "eFz" in Hamiltonian for the electron and LO-phonon interaction in electric field, does "z" show the position of the electron?

So when I first learned about Hamiltonians, my teacher presented them as something which you derived based Newton's second law, with the intermediate step of the Lagrangian. Doing it this way gets a Hamiltonian of the form H = T + V. Now I have a new teacher, who says that that these sorts of...

This is a question, not a homework problem, as i am currently studying for my test on classical mechanics suppose H = \sum_{i} \dot{q_{i}}(p,q,t) p_{i} - L(p,q,t) also i can prove that dH = \sum_{i} (\dot{q_{i}}dp_{i} - \dot{p_{i}} dq_{i}) - \frac{\partial L}{\partial t} dt suppose...

I am currently studying loop quantum gravity, and therefore GR in Ashtekar variables (A,E). I see the vector constraint E^a_iF^i_{ab}=0 is said to generate spatial diffeomorphisms (where F is the Yang-Mills field strength in terms of A), but how can I show this? How do spatial diffeomorphisms...

[x, H]= ?? Given the Hamilton operator for the simple harmonic oscilator H, how do I get to [X, H]= ih(P/ m)? I put X in momentum representation, but then I can't get rid of these diff operators. mmh? thanks in advance

please see the following Hamiltonian mode. two two-level atoms(or two qubits) interact with photon. á、à are the creation and annihilation operators of photon please rewriting H in the way of pauli operators , will looks very simple H = E1 ( |e1><e1| －|g1><g1| ) + E2 ( |e2><e2| －|g2><g2|...

Why is there no kinetic energy term in said hamiltonian? Suppose I take a magnetic dipole in my hand, and I throw it in the field. Then surely its classical energy is E = p²/2m - \vec{\mu} \cdot \vec{B}. Then why is the p²/2m term absent in the hamiltonian?

Spin Orbit Interaction Hamiltonian is defined as follows: H_{SO}=\frac{1}{2m_{e}c^2}\frac{1}{r} \left(\frac{\partial V}{\partial r}\right)L\cdot S How does one derive the above Spin Orbit Interaction Hamiltonian from relativistic treatment? Is there a good textbook that elaborates on...

Hi. Can anyone tell me what exactly the "Heisenberg Hamiltonian" is? I found it in an article related to: the renormalization group. Thanks in advance. Somy:smile:

How can I prove that the Hamiltonian commutes with the angular momentum operator? In spherical coordinates it is straightforward but I'd like to understand the physical meaning of it. Thanks.

http://www.arxiv.org/abs/gr-qc/0510011 "Recently the Master Constraint Programme (MCP) for Loop Quantum Gravity (LQG) was launched which replaces the infinite number of Hamiltonian constraints by a single Master constraint. The MCP is designed to overcome the complications associated with the...

I can't understand what the question is asking~ hope somebody can help me~ A particle of mass m moves in a plane under the influence of Newtonian gravitation force, described by the potential V(r) = - GmM/r (symbol in conventional meaning) Now introduce a new variable u(theta) = 1/r(theta)...

Consider the following general Hamiltonian for the electromagnetic field: H = \int dx^3 \frac{1}{2} E_i E_i + \frac{1}{4}F_{ij}F_{ij} + E_i \partial_i A_0 + \lambda E_0 where \lambda is a free parameter and E_0 is the canonical momentum associated to A_0, which defines a constraint (E_0 =...

Let be a Hamiltonian in the form H=T+V we don,t know if V is real or complex..all we know is that if E_n is an energy also E*_n=E_k will be another energy, my question is if this would imply V is real... my proof is taking normalized Eigenfunctions we would have that...

let,s suppose we have the Hamiltonian H=T+V but V is V=F(z) being z=a+ix then would the energies be real?..thanks.

sup, just realized there is not graphtheory/combinatorial subforums. is the hamiltonian cycle still considered and NP problem?

Can anyone give me a basic definition of Hamiltonian Mechanics without all the fancy mathematics, and perhaps could supply a few examples as to this? I am trying to make sense of this, but everywhere I go, I run into very large mathematical equations and no defintions I can understand...

I have a question regarding the Hamiltonian in a magnetic field. First Hamiltonian with potential V is given by Ho = (1/2m)*p^2 + V but if a vector potential A is also present then H1 = (1/2m)*(p+eA)^2 + V there is a way to write H1 interm of Ho H1 = exp(-ier.A) Ho exp(ier.A) where r...

I am not familiar with calculations such as the following one, and I want to be sure I do the right steps before going on with Peskin & Schröder. I want to derive step by step the Hamiltonian of the real scalar field. I have no problem to arrive at the first part of (2.31) in page 21: H =...

Hi ! I'm trying to solve the restricted problem of three bodies, where a negligeable mass particule is moving in the gravitationnal field of two heavy objects which are in circular orbit around their common center of mass. this is a plane problem... I describe the mouvment in the mobile...

Hamilton equations of flyball governor I'm trying to find 1. The Hamiltonian 2. The Hamilton equation of motion for the flyball governor shown in problem 2 here http://www.srl.caltech.edu/phys106/1999/Homework3.pdf This is what i have. Can someone tell me if I'm right...

I need some suggestions and/or corrections if I understand this correct? My questions are based on the book by Mandl and Shaw. Conserved currents are based on Noethers theorem and directly connected to spacetime and field transformations (rotations, translations, phase, ...). One can...

Generally we write H Y = E Y in quantum mechanics. Would it make any sense to use T ( stress-energy tensor) from general relativity and G (curvature) to write : T Y = G Y

I came cross this problem when solving some older tests from Classical Mechanics, so I was hoping anybody can help me. I have expression for relativistic lagrangian of a particle in some potential that is function only of coordinates and not velocities: L = - mc^2* sqrt( 1 - (x'^2 + y'^2 +...

Let say I have prepared two identical particle, both describable by a wavefunction Psi, whereby, Psi = a*1 + b*2, where, 1 and 2 are two stationary wavefunctions. If I perform an experiment to find out the systems' energy, this is equivalent to operating a Hamiltonian on Psi. Operating...

[H,P]=0 , where P is momentum operator. Hamiltonian is commutable with momentum operator. so H and p have wave function simultaniously, but in 1-dimensional potential well degeneracy not exist. what is the reason?

I was wondering: why is the SM always written with a Lagrangian? Couldn't you just as well write it with a Hamiltonian? The way I understand, the Lagrangian gives me the kinetic energy minus the potential energy (basically a measure for the "free energy", though not in the thermodynamical...