Help me in writting Hamiltonian of two dimensional oscillator with interaction
(**2)*(y**2) using only MATLAB .
Biswanath
I also do not uderstand the question It is not problem to write Hamiltonian: simply add two operators of kinetic energy The problem is how to solve the system of coupled nonlinear equations (in classical theory) or the differential equation in partial derivatives in quantum case
H=(p(x))^2 + (p(y))^2 + x^2 + y^2 +(x^2)*(y^2)
Help me to write the above Hamiltonian using MATLAB for calculation of energy .
The ground state energy is 2.195 918 .
I am unable to reproduce this result . I feel once you solve to get eigenvalues ,then
solution in classical physics becomes easy .
In classical physics the ground state energy would be given by the value of the potential energy for the values of x and y that correspond to its minimum value, i.e. p(x)=0, p(y)=0, 2x + 2x y2=0 and 2y + 2y x2=0, giving x=0 and y=0 and energy equal to 0, since y2+2, respectively x2+2, never vanishes.
To find the ground state energy, when quantum effects become relevant, one typically solves the Schrödinger equation. One can estimate the ground state energy by computing / = , where |ψ> is some linear combination of trial states (which comes down to the same thing).
One can, also, attempt to compute the ground state energy using perturbation theory about the ground state of the harmonic oscillator, treating the x2y2 term as a perturbation. One way might be to express the position operators in terms of the creation and annihilation operators of the harmonic oscillators and compute the expectation value of x2y2 in that vacuum. It won't vanish.
The expression given is that of the Hamiltonian, however, so the question seems strange.
Prof Feranchuk
Please write the Hamiltonian for eigenvalue calculation using Matlab.
Biswanath
To all
Help me to write the Hamiltonian for eigenvalue calculation using MATLAB
Usually I do not use Matlab However all necessary formulas for calculation of general case of coupled oscillators by means of operator method are written in my book "Nonperturbative description of quantum systems" Springer 2015
Prof Nicolis
Help me in writting Hamiltonian using MATLAB for eigenvalue calculation.
Prof Rath
Dear Wolfgang
Help me to write the Hamiltonian using Matlab for eigenvalue calculation.
Prof Rath
Dear Prof Nicolis
Have you now understood my problem ?
If so help in writting using MATLAB only .
Prof Rath
Prof Feranchuk
Actually I want to study resonance in 2D system. Now after retirement , it is difficult
to find your book and so also the approach .However before RS , I want to study
energy eigenvalues in 2D. Furthe,r if you have interest in RS , then inform me ,I will
send my work in 1D system.
Regards
Prof Rath
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