The central term in the hamiltonian formalism. Can be interpreted as an energy input, or "true" energy.

learn more… | top users | synonyms

7
votes
0answers
194 views

Role of physics in the zeta function $\zeta$ and the Riemann hypothesis

Hilbert and Polya suggested a physical way to verify the Riemann hypotesis about $\zeta(x)$. If the Riemann hypotesis is true, we can state all eigenvalues of physical problems are real. What is the ...
7
votes
0answers
652 views

Exact diagonalization by Bogoliubov transformation

I am developing a model of multiple gaps in a square lattice. I simplified the associated Hamiltonian to make it quadratic. In this approximation it is given by, $$ H = \begin{pmatrix} \xi_\mathbf{k} ...
5
votes
0answers
92 views

Hamiltonian Operator for nonrenormalizable Effective Field Theories?

Assuming we have a Effective Field Theory, for example a Real Scalar Field Theory, defined through a Lagrangian density of the form $\mathcal{L}_{eff} = \frac{1}{2}\partial_\mu\phi \partial^\mu\phi - ...
5
votes
0answers
85 views

CM: Need to recover the Hamiltonian, knowing conserved quantities and information about the EOM, possibly via action-angle coordinates

Statement of the problem: I have a system with 2 degrees of freedom and I have found two independent conserved quantities, without knowledge of the Hamiltonian. I'm looking for a method to recover a ...
4
votes
0answers
276 views

Ostrogradski’s theorem's proof

I am looking for a proof of the next theorem: "If the higher order time derivative Lagrangian is non-degenerate, there is at least one linear instability in the Hamiltonian of this system." Where ...
4
votes
0answers
224 views

Topological Quantum Field Theories

I've asked this on Math.SE, but with no avail. So, I decided to ask it here. I was wondering about the following after reading the Wikipedia article on TQFTs. It is said that TQFTs have vanishing ...
4
votes
0answers
101 views

Non-Hermiticity when Fourier transforming onto a finite lattice

I'm doing numerical simulations. I have the Haldane model in a honeycomb lattice where $$ H = \sum \limits_{<ij>}a^\dagger_i b_j + h.c $$ Where $i$ belongs to sublattice $A$, and $j$ to ...
3
votes
0answers
74 views

Liouville's theorem for systems with dissipation described by a single hamiltonian

Following this link, one can treat dissipation in the lagrangian by using a factor $e^{\frac{t \beta}{ m}}$ in addition to the Lagrangian $L_0$ of a system without disspation: $ L_0[q, \dot{q}] = \...
3
votes
0answers
319 views

What does it mean to expand a Hamiltonian using perturbation theory?

On UC Davis chemwiki website, the Hamiltonian for quadrupolar coupling in NMR is analyzed. (The details of this aren't important.) It is said in the analysis that: The expansion of the ...
2
votes
0answers
93 views

Transfer from Heisenberg to Ising model

It is well know, that ferromagnets can be described using Hamiltonian $$ H = -\sum\limits_{i<j}J_{ij}\, (\mathbf{s}_i \cdot \mathbf{s}_j). $$ where (three dimensional) spins $\mathbf{s}_i$ ...
2
votes
0answers
125 views

Fermion 1D Hubbard Model ground state in the U = 0 limit

I am trying to determine the ground state of the 1D fermionic Hubbard model at half-filling of $2L$ sites with $L$ electrons with spin-$\uparrow$ and $L$ electrons with spin-$\downarrow$ in the $U=0$ ...
2
votes
0answers
114 views

About the derivation of the Hamilton-Jacobi equation

It is an old question for me. In Goldstein's book, the H-J equation is derived in this way. We want to find a generating function $F(q,P,t)$ such that the transformed Hamiltonian vanishes identically, ...
2
votes
0answers
159 views

The proof that Dirac's hamiltonian commutes with inversion operator

I tried to check the statement that Dirac free Hamiltonian commutes with inversion operator. For $$ \hat {P}\Psi(\mathbf r , t) = i\hat {\gamma}_{0}\Psi (-\mathbf r , t), \quad \hat {H} = (\hat {\...
2
votes
0answers
155 views

Adiabatic quantum evolution of single photon or biphoton system

The prerequisite for adiabatic quantum evolution of single photon or biphoton system is as follows. We have to prepare a single photon or biphoton quantum system which has a ground and a higher level ...
2
votes
0answers
61 views

Spin Transition Energies

I am reading a paper: http://arxiv.org/ftp/arxiv/papers/1305/1305.2445.pdf On p. 22, the following Hamiltonian is given: $$ H = \mu_B g \mathbf{B} \cdot \mathbf{S} + D(S_Z^2+\frac{1}{3}S(S+1)) + E(...
2
votes
0answers
102 views

Boundary condition Hamiltonian with point tinteractions

I`m studying the Hamiltonian with point interaction centered in $y$ in three dimensions. I know that the elements in the domain of the Hamiltonian are of the form $$\psi=\phi+qG^z(\cdot-y)$$ where $G^...
1
vote
0answers
30 views

Minimum gap between consecutive energy levels?

Assume a standard one-particle, non-relativistic Hamiltonian of the form \begin{equation} H=\frac{p^2}{2m}+V(r) \end{equation} and denote its eigenvalues as $E_{n,\tau}$, where $n$ is the principal ...
1
vote
0answers
47 views

Normalizable eigenvectors of the inverted harmonic oscillator

Consider the inverted harmonic potential $V(x) = - x^2 $. Does the corresponding Hamiltonian $$ H = p^2 - x^2 $$ have any normalizable eigenstate? How about $$ H = p^2 - x^4 ? $$ Any good ...
1
vote
0answers
73 views

How to plot numerically the wave functions according to the Hamiltonian?

It is often difficult to analytically solve the Schrodinger equation, and so we need to obtain a solution numerically. An example plot is shown below. Here, the wave functions for a three junction ...
1
vote
0answers
30 views

Meaning of Hamiltonian between two different states

If we have states $\left | 1 \right>$ and $\left | 2 \right>$, and the Hamiltonian operator $\hat{H}$, what is the meaning of the expression $$\left< 1 \right | \hat{H} \left | 2 \right >$$...
1
vote
0answers
75 views

Bogoliubov transformation with two pairing terms

Let us assume that we have a Hamiltonian of the form: $$ H = \sum_{k,\sigma,s}\epsilon_{\sigma s}\left(k\right)c_{k\sigma s}^{\dagger}c_{k\sigma s} + \sum_{k,s}\Delta_{0}\left(k\right)c_{k\uparrow s}^...
1
vote
0answers
49 views

Eigenvalues of Hamiltonian with on-diagonal coordinate

A bit abstract, but if I take the standard graphene Hamiltonian (around the Dirac point) and introduce an on-diagonal term proportional to the coordinate $\hat{y}$, how would I find the eigenstates ...
1
vote
0answers
87 views

A mysterious conserved quantity for a central potential

In teaching a course in classical mechanics and I have come across (from my predecessor) a to me mysterious conserved quantity. We are considering a gravitational (or electric) potential with the ...
1
vote
0answers
73 views

Commutation between angular momentum and Hamiltonian

Consider the following Hamiltonian of a 3-dimensional system: $$H=\frac{p^2}{2m}+V(r)$$ If the components of the angular momentum, $L_i$, commute with $H$, then: $$[H,L_i]=0$$ This condition can ...
1
vote
0answers
19 views

ray tracing through a stack of flat plates

Say I want to trace rays in 3 dimensions through a stack of flat plates of various refractive indices. My rays have canonical coordinates {Q,P}. The plates are normal to the z axis, all the rays start ...
1
vote
0answers
80 views

The second order scalar quartic field theory Feynman diagrams

I'm trying to find the second order Feynman diagrams for the scattering of a scalar phion, described by the Lagrangian $$ L = L_0 + L_I \\ L_0 = \frac{1}{2}[\partial_{\mu} \phi(x)]^2 - \frac{1}{2}m^2 ...
1
vote
0answers
104 views

Derivation of Schrodinger equation using unitary operators

I encountered the derivation of Schrodinger time dependent equation using expansion of a unitary time propagation operator into power series in a small quantity $\delta t$, working to first order in $\...
1
vote
0answers
78 views

Hamiltonian in Majorana basis

I read (for example here: cond-mat/0010440) very often that if we transform the Hamiltonian from a fermionic basis to the basis of Majorana operators by expanding the fermionic operators in real and ...
1
vote
0answers
62 views

How geometry, and hence, a tight-binding Hamiltonian dictates the eigenvalues?

Considering an 'N' atom system, how should we understand the geometric dependence on the calculated eigenvalue spectrum by solving the nearest neighbor tight-binding Hamiltonian? A simple example ...
1
vote
0answers
79 views

Does the additivity property of Integrals of motion and Lagrangians valid in all situations?

I would like to know if the additivity property of an integral (constant) of motion valid in all situations ? It works for energy but does it work for all other integrals of motion in all kinds of ...
1
vote
0answers
122 views

Non Hermitian Quantum Mechanics

I was just reading about Non-Hermitian Quantum Mechanics dealing with Hamiltonians $H$ that are not Hermitian operators. Then it is unclear that we get orthonormal eigenstates. Now, I was reading a ...
1
vote
0answers
72 views

Exercise about Bethe Ansatz for $N=3$ particles on a ring of length $L$

Suppose there are $3$ bosons living on a 1-dimensional ring of length $L$. The Hamiltonian is given by $$H=-\sum_{i=1}^3\frac{\partial^2}{\partial x_i^2}+\sum_{1\leq j<k\leq 3}2c\delta(x_j-x_k).$$...
1
vote
0answers
99 views

Basis spin states

We are given a system of $N$ spin states and the following (non-hermitian) Hamiltonian $$H = \frac{N \hbar \nu}{2M} \sin(\alpha)+ \sum_{i=1}^N \frac{\hbar \omega_i }{2} \sigma_{z,i} + \frac{\hbar \nu ...
1
vote
0answers
107 views

What happens to the Hamiltonian of the wave function after measurement?

As I understand it, the Hamiltonian is the kinetic plus the potential energy of the wave function. When a measurement is done what happens to the kinetic and potential energy? Does it dissipate? Is ...
1
vote
0answers
63 views

What is the physical significance of the two integration constants that appear in the ladder operator decomposition of the Quantum Hamiltonian?

If I have a simple one dimensional Hamiltonian of the form \begin{align} H = V - \partial_x^2 \end{align} and if I know one zero energy state solution $H\psi_0=0$ then I can use the Wronskian to ...
1
vote
0answers
75 views

What does the relation between mass and energy of a free particle mean?

What does the Hamiltonian for a free particle mean? Does it mean that the kinetic energy of the particle is in reverse relation with mass? $H$ or $E=\hbar^{2}k^{2}/2m$. Or better to ask: what's the ...
1
vote
0answers
85 views

Contradiction in classical analysis of the hamiltonian $\mathcal{H}=xp$?

I am writing an essay on the Berry Keating article proposing to use the $\mathcal{H}=xp$ hamiltonian to get a correspondence between the nontrivial riemann zeros and the eigenvalues of an Hermitian ...
1
vote
0answers
63 views

Showing the Hamiltonian of the $\alpha$ FPU is real

I am studying the $\alpha$ FPU chain which is a model of coupled oscillators with small non-linearity. For these systems, I derived the following Hamiltonian $H$ which is given by $$ H=\sum_{j=1}^{N} \...
1
vote
0answers
214 views

Second quantization Hamiltonian Matrix for an aggregate

I am working on the matrix form of the Hamiltonian in the second quantization. I haven't taken any course on second quantization and I'm learning it on my own. I'm a little bit confused about the ...
1
vote
0answers
89 views

Exotic coupling

I have encountered the minimal coupling between a field and charges before $$H = \frac{1}{2m}(p-qA)^2,$$ whereby I am considering the classical case. The description minimal leads me to ask if ...
1
vote
0answers
597 views

Anharmonic oscillator solution function

I am solving a CLASSICAL an-harmonic oscillator problem with Hamiltonian given by $H= (1/2)\dot{x}^2+(1/2)x^2-(1/2)x^4$ with all the constants (k's) and mass being taken as 1 (one). I find that $x= \...
1
vote
0answers
115 views

What is the difference between broken and unbroken sypersymmetry?

In a physics article I read recently, the author introduces the notion of supersymmetry by saying basically that the system described by the Hamiltonian $H$ is supersymmetric if $H$ can be decomposed ...
1
vote
0answers
350 views

What is the energy scale of a Hamiltonian?

On the second page of this paper a term 'fundamental energy scale' is used while talking about a Hamiltonian. The context is implementing Deutsch's algorithm using Adiabatic Quantum Computation. What ...
1
vote
0answers
44 views

Delivered/Reflected Power by Drive on a Hamiltonian System

Imagine a SHO with a drive F(t). (or in general a Hamiltonian system) What is the power delivered to the system and can we talk about the power reflected? is i am imagining say a MW oscillator ...
1
vote
0answers
128 views

Measurement in Quantum mechanics

I have got a quantum conservative system whose Hamiltonian is $H$. I consider an selfandjoint operator $O$ whose eigenvalues and eigenvectors are: $$O|\psi _{n}\rangle = \lambda _{n}|\psi _{n}\rangle$$...
1
vote
0answers
66 views

Length of the orbit (semiclassical orbits)

The Gutzwiller trace is about $$ d(E)=d_{0} (E)+ \sum_{p.o}A_{p}Cos(S(E)\ell_{p}) $$ and $ \ell_{p} $ are the length of the orbit. However my question is, how can one derive the length of the orbit ...
0
votes
0answers
36 views

Systems with extensive ground state degeneracy

This is sort of a follow up to this question: What does it mean for a Hamiltonian or system to be gapped or gapless? There it is stated in one of the answers that a system is gapped if it fulfills ...
0
votes
0answers
17 views

Properties of non-commuting (and particularly anti-commuting) operators

The commutator of 2 operators describes in some sense "how much" do they commute or actually its more about "how far" are they from commuting. The case where the commutator of 2 operators (say ...
0
votes
0answers
20 views

Eigen energy of the Landau levels in a tilted magnetic field

The problem pertains to a fermi gas in a tilted magnetic field confined by a harmonic potential in the z direction. I chose the vector potential $(0,ax-bz,0)$. I obtain the following hamiltonain with ...
0
votes
0answers
30 views

Finding the initial state in the power method for Hamiltonian diagonalization

In section III of the lecture note Chapter 1: Exact Diagonalization, Weimer has described the Power method for Hamiltonian diagonalization. The process requires the choice of an random initial state ...