Hamiltonian Definition and 901 Threads

I came across a previous exam question which stated: Do all physical states, ψ, abide to Hψ = Eψ. I thought about it for a while, but I'm not really sure.

Hello, This was part of my midterm exam that i couldn't solve. Any help is extremely appreciated. Problem: The K.E. of a rotating top is given as L^2/2I where L is its angular momentum and I is its moment of inertia. Consider a charged top placed at a constant magnetic field. Assume that the...

I'm a little confused about the hamiltonian. Once you have the hamiltonian how can you find conserved quantities. I understand that if it has no explicit dependence on time then the hamiltonian itself is conserved, but how would you get specific conservation laws from this? Many thanks

For each of the four fundamental forces (or fields), must one always specify the Lagrangian and Hamiltonian? What else must one specify for other fields (like the Higgs Fields)?

Hey, here's a quick question: What is the Hamiltonian operator corresponding to a decaying Carbon-14 atom. Any insight is quite appreciated!

Homework Statement [/B] Particle is moving in 2D harmonic potential with Hamiltonian: H_0 = \frac{1}{2m} (p_x^2+p_y^2)+ \frac{1}{2}m \omega^2 (x^2+4y^2) a) Find eigenvalues, eigenfunctions and degeneracy of ground, first and second excited state. b) How does \Delta H = \lambda x^2y split...

Homework Statement [/B] Particle in one dimensional box, with potential ##V(x) = 0 , 0 \leq x \leq L## and infinity outside. ##\psi (x,t) = \frac{1}{\sqrt{8}} (\sqrt{5} \psi_1 (x,t) + i \sqrt{3} \psi_3 (x,t))## Calculate the expectation value of the Hamilton operator ##\hat{H}## . Compare it...

I'm reading about stationary states in QM and the following line, when discussing the time-independent, one-dimensional, non-relativist Schrodinger eqn, normalization or the lack thereof, and the Hamiltonian, this is mentioned: "In the spectrum of a Hamiltonian, localized energy eigenstates are...

suppose that the momentum operator \hat p is acting on a momentum eigenstate | p \rangle such that we have the eigenvalue equation \hat p | p \rangle = p| p \rangle Now let's project \langle x | on the equation above and use the completeness relation \int | x\rangle \langle x | dx =\hat I we...

Hello everybody, As I mentioned in the title, it is about molecular symmetry and its Hamiltonian. My question is simple: For any molecule that belong to a precise point symmetry group. Is the Hamiltonian of this molecule commute with all the symmetry element of its point symmetry group...

I am reading an article on Arxiv about modelling the electron structure in a nanowire crystal: http://arxiv.org/abs/1511.08044 But I am having trouble understanding the hamiltonians (1) and (2). In (1) what is the purpose of the term E_gap/2. Is that just a reference point for the energy or...

I am working with the general Hamiltonian for an electron gas of density ρ(r): H = -ħ2/2m∑∂2/∂xi2 + 1/4πε ∫dr∫dr' ρ(r)ρ(r')/lx-x'l I wonna do a Hartree Fock approximation on this Hamiltonian. How does that work in general?

Hi everyone, I need help for preparing a Hamiltonian matrix. What will be the elements of the hamiltonian matrix of the following Schrodinger equation (for two electrons in a 1D infinite well): -\frac{ħ^{2}}{2m}(\frac{d^{2}ψ(x_1,x_2)}{dx_1^{2}}+\frac{d^{2}ψ(x_1,x_2)}{dx_2^{2}}) +...

Homework Statement I am trying to get the hamiltonain operator equality for a rigid rotor. But I don't get it. Please see the red text in the bottom for my direct problem. The rest is just the derivation I used from classical mechanics. Homework Equations By using algebra we obtain: By...

Homework Statement Define n=(x + iy)/(2)½L and ñ=(x - iy)/(2)½L. Also, ∂n = L(∂x - i ∂y)/(2)½ and ∂ñ = L(∂x + i ∂y)/(2)½. with ∂n=∂/∂n, ∂x=∂/∂x, ∂y=∂/∂y, and L being the magnetic length. a=(1/2)ñ+∂n and a†=(1/2)n -∂ñ a and a† are the lowering and raising operators of quantum mechanics. Show...

Homework Statement Homework Equations $$E_n^{(2)}=\sum_{k\neq n}\frac{|H_{kn}'|^2}{E_n^{(0)}-e_k^{(0)}}$$ The Attempt at a Solution Not sure where to start here. The question doesn't give any information about the unperturbed Hamiltonian. Some guidance on the direction would be great...

Homework Statement Point transformation in a system with 2 degrees of freedom is: $$Q_1=q_1^2\\Q_2=q_q+q_2$$ a) find the most general $P_1$ and $P_2$ such that overall transformation is canonical b) Show that for some $P_1$ and $P_2$ the hamiltonain...

Hello! I have recently bought the book The Principle of Relativity by Einstein (Along with Minkowski, Lorentz and Weyl). This book is simply a collection of papers published by Einstein (along with the other three scientists mentioned) concerning the development of Special and General...

Homework Statement Show that for the one-dimensional linear harmonic oscillator the Hamiltonian is: [; H = \frac{1}{2}[P^2+\omega ^2 X^2]-\frac{1}{2}\omega \hbar ;] [; =\frac{1}{2}[P+i\omega X][P-i\omega X]+\frac{1}{2} \omega \hbar ;] where P, X are the momentum and position operators...

Hi. I am working through a QFT book and it gives the relativistic Lagrangian for a free particle as L = -mc2/γ. This doesn't seem consistent with the classical equation L = T - V as it gives a negative kinetic energy ? If L = T - V doesn't apply relativistically then why does the Hamiltonian H =...

Hi all, This is the problem I want to share with you. We have the hamiltonian H=aP+bm, which we are commuting with the position x and take: [x,H]=ia, (ħ=1) Ok. Now if we take, instead of x, the operator X=Π+ x Π+ +Π-xΠ- where Π± projects on states of positive or negative energy the...

Homework Statement Given H=\frac{1}{2m}\left[ \vec{P}-q\vec{A}\right] ^{2}+qU+\frac{q\hbar }{2m}\vec{\sigma}.\vec{B} ..(1) show that it can be written in this form; H=\frac{1}{2m}\left\{ \vec{\sigma}.\left[ \vec{P}-q\vec{A}\right] \right\}^{2}+qU ...(2) Homework Equations [/B] In my...

This is what I have so far: I'm trying to show that the matrix D has to be unitary. It is the matrix that transforms the wavefunction.

I am reading Frohlic's paper on electron-phonon interaction. Frohlic.http://rspa.royalsocietypublishing.org/content/royprsa/215/1122/291.full.pdf Here author has introduced the quantization for complex B field in this paper and claimed to have arrived at the diagonalized form of the...

Homework Statement I am asked to find the Hamiltonian of a system with the following Lagrangian: ##L=\frac{m}{2}[l^2\dot\theta^2+\dot{\tilde{y}}^2+2l\dot{\tilde{y}}\dot{\theta}\sin{\theta}]-mg[\tilde{y}-l\cos{\theta}]## Homework Equations ##H = \dot{q_i}\frac{\partial L}{\partial...

Homework Statement Given a non-hermitian hamiltonian with V = (Re)V -i(Im)V. By deriving the conservation of probability, it can be shown that the total probability of finding a system/particle decreases exponentially as e(-2*ImV*t)/ħ Homework Equations Schrodinger Eqn, conservation of...

Using the Feshbach-Villars transformation, its possible to write the KG equation as two coupled equations in terms of two fields as below: ## i\partial_t \phi_1=-\frac{1}{2m} \nabla^2(\phi_1+\phi_2)+m\phi_1## ## i\partial_t \phi_2=\frac{1}{2m} \nabla^2(\phi_1+\phi_2)-m\phi_2## Then we can...

Hello. I'm studying quantization of electromagnetic field (to see photon!) and on the way to reach harmonic oscillator Hamiltonian as a final stage, sudden transition that the Fourier components of vector potential A become quantum operators is observed. (See...

Hi guys, I consider the qm-derivation of the electronic states of hydrogen. There are two different derivations (I consider only the coulomb-force): 1) the proton is very heavy, so one can neglect the movement 2) the proton moves a little bit, so one uses the relative mass ##\mu## The...

Hello everyone! I'm trying to follow a solution to a problem from the book "Problems and Solutions on Quantum Mechanics", it's problem 1017. There's a step where they go on too fast, and I can't follow. I've posted the solution and where my problem is down below. Homework Statement The dynamics...

Hello everyone, I m currently working on a problem that is freaking me out a bit, suppose I have a second quantized hamiltonian: \begin{eqnarray} H=H_{0}+ \epsilon d^{\dagger}d + V(d{\dagger}c_{0} + h.c) \end{eqnarray} In terms of some new operators, I would like to rotate the hamiltonian, so...

I came across a technique called "multiple-scale analysis" https://en.wikipedia.org/wiki/Multiple-scale_analysis where the equation of motion involves a small parameter and it is possible to obtain an approximate solution in the time scale of $$\epsilon t$$. I am wondering if it is possible to...

hi, i have studied the annihilation and creation operators and number operator N in relation with the simple harmonic oscillator that is governed by: H = hw(N+1/2) i don't understand the relation between the harmonic oscillator and for example, this hamiltonian: H = hw1a+a+hw2a+a+aa that i...

Homework Statement Consider the quantum mechanical Hamiltonian ##H##. Using the commutation relations of the fields and conjugate momenta , show that if ##F## is a polynomial of the fields##\Phi## and ##\Pi## then ##[H,F]-i \partial_0 F## Homework Equations For KG we have: ##H=\frac{1}{2} \int...

Hi, I am learning classical mechanics right now, Particularly Noether's theorem. What I understood was that those kinds of transformations under which the the Hamiltonian framework remains unchanged, were the key to finding constants of motion. But here are my Questions: 1. What is...

As far as I know, the Hamiltonian of graphene in the Bloch's sums |A\rangle and |B\rangle near the points K or K' is a 2 \times 2 matrix with the components: \langle A|H|A\rangle, \langle A|H|B\rangle, \langle B|H|A\rangle,\langle B|H|B\rangle which all are parameters (and not variables). But in...

Homework Statement How can I solve this hamiltonian equation? H= p2/2m +α/ħ (σxpy - σypx) + γ/ħ (σxpx - σypy) + βxσx + βyσy Homework Equations Rashba coupling effect equation: HR=α(σykx - σxky) The Attempt at a Solution H0=ħ2k2/2m + HR+ HD

Homework Statement H=\sum^N_{i=1}(\frac{p_i^2}{2m}+\frac{1}{2}(x_{i+1}-x_i)^2+(1-\cos(2\pi x_i)) Homework Equations Hamilton equation of motion I suppose ##\dot{q}=\frac{\partial H}{\partial p}## ##\dot{p}=-\frac{\partial H}{\partial q}##[/B]The Attempt at a Solution If particles are...

is there a generally accepted candidate Hamiltonian for LQG? i've seen marcus post these papers recently http://arxiv.org/abs/1507.00986 New Hamiltonian constraint operator for loop quantum gravity Jinsong Yang, Yongge Ma (Submitted on 3 Jul 2015) A new symmetric Hamiltonian constraint...

V Chernyak, Wei Min Zhang, S Mukamel, J Chem Phys Vol. 109, 9587 (can download here http://mukamel.ps.uci.edu/publications/pdfs/347.pdf ) Eq.(2.2), Eq. (B1) Eq.(B4)-(B6). When I substitue Eq.(B4)-(B6) into Eq.(2.2), I can not recover Eq.(B1). Who can give me a reference or hint on how to write...

Pretty straightforward question. The Einstein-Hilbert Action says that the Lagrangian for Gravity is ##L=R(-g)^{1/2}## where ##g## is the determinant of the Metric Tensor and ##R## is the Ricci Scalar (Actually I am not sure if the determinant of the metric should be included there). From this...

I am trying to teach myself DFT (yet again) from books and my maths is only improving at a modest pace to understand how people calculate using QM. So a very basic question now. When a Hamiltonian for a many body system is written as given in page 8 on this presentation...

According to <x|H|x\prime>=(-\hbar ^2 /2m \frac{\partial^2 }{\partial x^2}+v(x)) \delta (x-x\prime) can one draw the conclusion that the Hamiltonian is always diagonal in the position basis?

Homework Statement A particle of mass m moves in a "central potential" , V(r), where r denotes the radial displacement of the particle from a fixed origin. From Hamilton´s equations, obtain a "one-dimensional" equation for {\dot p_r}, in the form {{\dot p}_r} = - \frac{\partial }{{\partial...

All I know is that Lagrangian is kinetic energy- potential energy and Hamiltonian is kinetic energy + Potential energy. Why do we calculate the lagrangian or hamiltonian?

/How can I show that Potts model hamiltonian is equal to this matrix hamiltonian? Potts have these situations : { 1 or 1 or 1 or 0 or 0 or 0} but the matrix hamiltonian : { 1 or 1 or 1 or -1/2 or -1/2 or -1/2} I take some example and couldn't find how they can be equal.

Homework Statement Derive the Hamiltonian equation in terms of momentum and position ( p and r) for the given system whose lagrangian is stated as L=ř^2/(2w) - wr^2/2 Homework Equations L=ř^2/(2w) - wr^2/2 and H=př-L The Attempt at a Solution Notice here ř means first derivative of r. As i...

Why is Hamiltonian defined as 1st derivative with respect to time ? From the units of energy (kgm2s-2) I would expect it to be defined as 2nd derivative with respect to time. (I'm reading http://feynmanlectures.caltech.edu/III_11.html#Ch11-S2)

In weak field regime i know that it is possible to quantize the gravitational field obtaining a quantum theory of free particles, called gravitons, which is very similar to the one for the electtromagnetic field. Do you know some book in wiich i can study this theory? In anycase what is the...

Homework Statement The e-states of H^0 are phi_1 = (1, 0, 0) , phi_2 = (0,1,0), phi_3 = (0,0,1) *all columns with e-values E_1, E_2 and E_3 respectively. Each are subject to the perturbation H' = beta (0 1 0 1 0 1 0 1 0) where beta is a positive constant...