Hamiltonian Definition and 833 Threads

I am new to quantum physics. My question is how to write the Hamiltonian in dirac notation for 3 different states say a , b , c having same energy. I started with Eigenvaluee problem H|Psi> = E|psi> H = ? for state a? SO it means that indvdually H= E (|a><a|) for state a and for all three...

I am solving a Hamiltonian including a term \begin{equation}(x\cdot S)^2\end{equation} The Hamiltonian is like this form: \begin{equation} H=L\cdot S+(x\cdot S)^2 \end{equation} where L is angular momentum operator and S is spin operator. The eigenvalue for \begin{equation}L^2 ...

Homework Statement Find the matrix elements of the Hamiltonian in the energy basis for the ISW. Is it diagonal? Do you expect it to be diagonal? Homework Equations H=\frac{p^2}{2m}+V \frac{d}{dt}\langle Q \rangle = \frac{i}{\hbar} \langle[\hat H, \hat Q] \rangle + \langle...

My question is simple is every classical mechanics problem which is solvable by Lagrangian & Hamiltonian methods also solvable by Newtonian methods of forces and torques? And why does it seem that LH make solutions to be a lot more easier than Newtonian methods, and is it always this way?

Homework Statement I have the state: |\psi>=cos(\theta)|0>+sin(\theta)|1> where \theta is an arbitrary real number and |\psi> is normalized. And |0> and |1> refer to the ground state and first excited state of the harmonic oscillator. Calculate the expectation value of the Hamiltonian...

A textbook gives the following interaction Hamiltonian describing the interaction of an atom (having transition dipole moment \mu) with a photon whose polarization can be \epsilon_{1} or \epsilon_{2}): H = g \Sigma^{2}_{s=1}\mu\bullet\epsilons\sigma^{-}a^{+}_{s} + h.c. where \sigma^{-} is...

Homework Statement Suppose the potential in a problem of one degree of freedom is linearly dependent on time such that the Hamiltonian has the form: H= p^2/2m - mAtq where m is the mass of the object and A is contant Using Hamilton's canonical equations that are give below. Find the...

Hi all, I've a hamiltonian that describes the coupling of electrons in a crystal (bloch electrons) to an EM field described by a vector potential A \begin{equation} \mathscr{H} = \frac{e}{mc}\left[\mathbf{p}(-\mathbf{k}) \cdot \mathbf{A}(\mathbf{k}, \omega)\right] \end{equation}...

Can anyone explain how the time evolution operator commutes with the Hamiltonian of a system ( given that the the Hamiltonian does not depend explicitly on t ) ?

Homework Statement Show that the Hamiltonian operator (\hat{H})=-((\hbar/2m) d2/dx2 + V(x)) is hermitian. Assume V(x) is real Homework Equations A Hermitian operator \hat{O}, satisfies the equation <\hat{O}>=<\hat{O}>* or ∫\Psi*(x,t)\hat{O}\Psi(x,t)dx =...

Hi there, just wondered if anyone could help me... If I am given a hamiltonian describing a particle in one dimension H=p^2/2m +1/2 (γ(x-a)^1/2) + K(x-b) how do I go about finding the eigenstates and eigenvalues of this hamiltonian? Many thanks

Hi , I can't understand the general formula for weyl ordering of the hamiltonian . It is written in Srednicki field theory book in page 68 . Can someone explain how to derive this formula ?

Hello again everyone! I would like to ask a question regarding this Hamiltonian that I encountered. The form is H = Aa^+a + B(a^+ + a). Then there is this question asking for the eigenvalues and ground state wavefunction in the coordinate basis. The only given conditions are, the commutator...

In page (3) of the next link:http://www.phy.bris.ac.uk/people/berry_mv/the_papers/Berry401.pdf he writes that one can transform the hamiltonian H=xp to p^2-x^2 with a simple rotation transformation. Which one is that?

Watching this lecture from nptel about NP completeness: http://www.youtube.com/watch?v=76n4BjlL1cs&feature=player_embedded -We have an algorithm, HC , which given a graph tells us whether or not it has a hamiltonian cycle. -We want to use it in order to create an algorithm that determines...

I am reading about the recovery of some classical rules from quantum mechanics. My text (Shankar) considers a Hamiltonian operator in a one-dimensional space H = P^2 / 2m + V(X) where P and X are the momentum and position operators respectively. It then asserts that [X,H] = [X,P^2/2m]...

Hi everyone! I am answering this problem which is about the eigenvalues and eigenfunctions of the Hamiltonian given as: H = 5/3(a+a) + 2/3(a^2 + a+^2), where a and a+ are the ladder operators. It was given that a = (x + ip)/√2 and a+ = (x - ip)/√2. Furthermore, x and p satisfies the...

Hello, I am trying to write a program that will automate the creation of a tight binding Hamiltonian matrix for armchair cut graphene. However, I have almost no experience coding and would need some help to get started. This would be assuming that the energy between nearest neighbor carbon...

I have been reading about the derivation of the Hamiltonian from the Lagrangian using a Legendre transform. The Lagrangian is a variable whose value, by definition, is independent of the coordinates used to express it. (The Lagrangian is defined by means of a formula in one set of coordinates...

Hey guys (this is not a HW problem, just general discussion about the solution that is not required for the assignment), So I am doing this problem where I had to find the eigenvalues and eigenvectors of the Hamiltonian: H = A*S_{x}^{2} + B*S_{y}^{2} + C*S_{z}^{2}. Easy enough, just...

hai everyone, the question is " the hamiltonian of a particle is H = [(p*p)/2m + pq] where q is the generalised coordinate and p is the corresponding canonical momentum. the lagragean is ....? i know that H = p(dq/dt) - L. but the answer should not contain p. how can i solve it? answer is...

Hi all, My question is why Dirac's Hamiltonian isn't diagonal? As much as I understand, the momentum of the particle and it's spin belong to the complete set of commuting variables, which define the state of the particle, and their eigenstates must also be energy eigenstates. But because...

Hello: I am trying to understand how to build a hamiltonian for a general system and figure it is best to start with a simple system (e.g. a harmonic oscillator) first before moving on to a more abstract understanding. My end goal is to understand them enough so that I can move to symplectic...

Homework Statement A point of mass m is placed on a frictionless plane that is tangent to the Earth’s surface. Determine Hamilton’s equations taking: (a) the distance x (b) the angle q as the generalized coordinate. Homework Equations The Attempt at a Solution Take the...

Homework Statement Hello, I would like to derive geodesics equations from hamiltonian H=\frac{1}{2}g^{\mu\nu}p_{\mu}p_{\nu} using hamiltonian equations. A similar case are lagrangian equations. With the definition L=g_{\mu\nu}\dot{x}^\mu\dot{x}^\nu I tried to solve the...

Homework Statement Write down the Hamiltonian and its corresponding Hamilton equations for a particle in a central potential. Find the solution to the Kepler problem in this description.Homework Equations Hamiltonian. The Hamilton equations or motion equations are \dot q _i = \frac{\partial...

Homework Statement Determine the Hamiltonian corresponding to the an-harmonic oscillator having the Lagrangian L(x,\dot x )=\frac{\dot x ^2}{2}-\frac{\omega ^2 x^2}{2}-\alpha x^3 + \beta x \dot x ^2. Homework Equations H(q,p,t)=\sum p_i \dot q _i -L. p _i=\frac{\partial L}{\partial \dot...

Please correct me if I make any mistakes along the way. Suppose we have a simple tight-binding Hamiltonian H=\sum_i \epsilon _i c_i^\dagger c_i - t\sum_{\langle i j\rangle} c_i^\dagger c_j + h.c., In half-filling systems, we tend to impose a constraint such that each site has only one...

To prove: Commutator of the Hamiltonian with Position: i have been trying to solve, but i am getting a factor of 2 in the denominator carried from p2/2m Commutator of the Hamiltonian with Momentum: i am not able to proceed at all... Kindly help.. :(

Homework Statement This is a simple problem I thought of and I'm get a nonsensical answer. I'm not sure where I'm going wrong in the calculation. Find the value of <-,p',v';+,q',r'|H|-,p,v;+,q,r> where H is the free-field Dirac Hamiltonian H =...

Hello everyone I have difficulties in understanding some stuff in Lagrangian and Hamiltonian mechanics. This concerns the equations : \dot p = - \frac{\partial H}{\partial q} \frac{d}{dt} \frac{\partial L}{\partial \dot q} = \frac{\partial L}{\partial q} First I have to say that I'm a math...

Homework Statement Hi, I must find eigenvalues and eigenvector of this Hamiltonian, which describes a system of two 1/2-spin particles. H = A(S_{1z} - S_{2z}) + B(S_{1} · S_{2}) where S_{1} and S_{2} are the two spins, S_{1z} and S_{2z} are their z-components, and A and B are constants...

In most of the physical systems, if we have a Lagrangian L(q,\dot{q}), we can define conjugate momentum p=\frac{\partial L}{\partial{\dot{q}}}, then we can obtain the Hamiltonian via Legendre transform H(p,q)=p\dot{q}-L. A important point is to write \dot{q} as a function of p. However, for the...

In Greiner & Muller's 'Quantum Mechanics: Symmetries' (section 3.5) they explain that where a system possesses a symmetry, the corresponding Hamiltonian must be 'built up' from the Casimir operators of the corresponding symmetry group. Does anyone know of a reference where this is gone into...

This Hamiltonian popped up when I was reading an article, as a reference(wikipedia): http://en.wikipedia.org/wiki/Jaynes%E2%80%93Cummings_model#cite_note-1 I don't understand why the Hamiltonian \hat H_{atom} and \hat H_{int} look the way they are. Usually we we just take a classical Hamiltonian...

Hey, I am looking at the coupling hamiltonian for electrons in an EM field. In particular I'm interested in the inelastic scattering (this isn't the dominant part for inelastic scattering but it's confusing me). The part of the hamiltonian in the time/space domain that I'm interested in is...

Problem: ----------- I’m trying to understand how to generally find Eigen functions/values (either analytically or numerically) for Hamiltonian with creation/annihilation operators in many-body problems. Procedures: -------------- 1. I setup a simple case of finite-potential well...

It's given as this H\left(q_i,p_j,t\right) = \sum_m \dot{q}_m p_m - L(q_i,\dot q_j(q_h, p_k),t) \,. But if it's a Legendre transformation, then couldn't you also do this? H\left(q_i,p_j,t\right) = \sum_m \dot{p}_m q_m - L(p_i,\dot p_j(p_h, q_k),t) \,.

Homework Statement A system with two spins of magnitude 1/2 have spin operators S1 and S2 and total spin S = S1 + S2 B is a B-field in the z direction (0,0,B) The Hamiltonian for the system is given by H = m S1 . S2 + c B.S where m,c are constants. By writing the Hamiltonian in...

I am having trouble typing the Hamiltonian symbol into latex. I found the symbol in the http://mirrors.med.harvard.edu/ctan/info/symbols/comprehensive/symbols-a4.pdf" , however, I had some difficulties in installing the font and stuff. I am using tex-live. I got the following error...

What is the difference between the Hamiltonian operator and the Total energy operator? If both is used when working with total energy, why are there two different operators?

When dealing with the Euler-Lagrange equation in a physical setting, one usually uses the Hamiltonian L=T-V as the value to be extremized. What is the physical interpretation of the extremizing of this value?

When applying Noether's theorem to a coil of wire under reflection transformation invariance, what Hamiltonian would one use as as the extermized function? I realize that electromagnetism is not invariant over reflection transformations, that's what I am trying to prove.

Homework Statement Hi Say I have a Hamiltonian given by H = δSz acting on my system, where δ is a random variable controlled by some fluctuations in my environment. I have to show that if I start out with <Sx>=½, then the Hamiltonian will reduce <Sx> to <Sx> = ½<cos(δt)> where the <>...

Lets say H = \frac{m}{2} (\dot{Q}^2 - \omega^2 Q^2 ) where Q is the generalized coordinate. It doesn't explicitly depend on time, but the Q and the \dot{Q} does. If i differentiate it with respect to time it should be zero if it's constant, right? So i guess my question is should i treat the Q's...

trying to get the open string hamiltonian I use H=\int\,d\sigma(\dot{X}.P_{\tau}-L)=\frac{T}{2}\int(\dot{X}^{2}+X'^{2})d\sigma as in Witten´s book, but we are integrating the Virasoro constraint equal to zero. So, Is not the Hamiltonian zero? Please, clarifyme this equation.

Hamiltonian H=\frac{1}{2m}(P+\frac{e}{c}A)^{2} - e\phi and H^{'}=\frac{1}{2m}(P+\frac{e}{c}A^{'})^{2} - e\phi^{'} With gauge: A^{'}=A+\nabla\chi and \phi^{'}=\phi-\frac{1}{c}\dot{\chi} Why H^{'}-\frac{e}{c}\dot{\chi}=e^{-\frac{ie\chi}{\hbar c}}He^{\frac{ie\chi}{\hbar c}} ? Thanks.

I have a question. What is the definition of Heisenberg hamiltonian? \hat{H}=-\sum_{i,j}J_{i,j}\hat{\bfs{S}}_i\cdot \hat{\bfs{S}}_j or \hat{H}=-2\sum_{i,j}J_{i,j}\hat{\bfs{S}}_i\cdot \hat{\bfs{S}}_j or \hat{H}=\sum_{i,j}J_{i,j}\hat{\bfs{S}}_i\cdot \hat{\bfs{S}}_j or...

I'm researching General Relativity and have stumbled upon a bit of Hamiltonian mechanics. I roughly understand the idea behind the Hamiltonian of a system, but I'm utterly confused as to what the hell a Hamiltonian vector field is. I've taken ODE's, PDE's, Linear Algebra, and I'm just being...

Hi there, physics lovers. I'm studying field theory. So far, so well. I got it with the lagrangian density. I understood it. But then I DIDN'T FIND stuff about the Hamiltonian density. I couldn't find anything in Landau-Lifgarbagez series, and that makes me worry. I've been looking in the...