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- If we have two operators A and B possess the same common Eigen function, then prove that the two operators commute with each otherEvaluate the commutator [Â,B̂] of the following operators.Show that the function ψ = 8e5x is an eigenfunction of the operator d/dx. What is the eigenvalue? Prove that the momentum operator corresponding to px is a Hermitian operator. Show solutions please. thanks!
- What do you mean by pauli's spin matrices? Show that Pauli's spin matrices are hermitian and obey the commutation relation given in the imageThe energy of the Hamiltonian operator defined below for the one-dimensional anharmonic oscillator Calculate first-order contributions to eigenvalues. (Here ? is a small number.)A point particle moves in space under the influence of a force derivablefrom a generalized potential of the formU(r, v) = V (r) + σ · L,where r is the radius vector from a fixed point, L is the angular momentumabout that point, and σ is the fixed vector in space. Find the components of the force on the particle in spherical polar coordinates, on the basis of the equation for the components of the generalized force Qj: Qj = −∂U/∂qj + d/dt (∂U/∂q˙j)
- Show that the total energy eigenfunctions ψ210(r, θ, φ) and ψ211(r, θ, φ) are orthogonal. Doyou have to integrate over all three variables to show this?Show that the operator H = -1/2(d^2/dx^2) is hermitian, assuming that it operates on a Hilbert space of L^2 functions whose functions and derivatives vanish at x = −∞ and x = +∞show hamiltonian operator for the plane waves (exponential, imaginary) Prove that this operator does not change this function. Prove that this operator does generate energy of a particle in free space.
