Final answer:
The Hamiltonian for an isotropic harmonic oscillator in two dimensions is given by (px^2 + py^2)/(2m) + (kx^2 + ky^2)(x^2 + y^2)/(2), where px and py are the momenta in the x and y directions respectively, m is the mass of the oscillator, kx and ky are the spring constants in the x and y directions respectively, and x and y are the displacements in the x and y directions respectively.
Step-by-step explanation:
The Hamiltonian for an isotropic harmonic oscillator in two dimensions is given by:
H = (px2 + py2)/(2m) + (kx2 + ky2)(x2 + y2)/(2)
where p x and p y are the momenta in the x and y directions respectively, m is the mass of the oscillator, k x and k y are the spring constants in the x and y directions respectively, and x and y are the displacements in the x and y directions respectively.