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Quantum-Mechanics Questions
Quantum-Mechanics Questions
Find the energy levels and wave functions of a particle in a potential field
Perturbation theory
Quantum chemistry
5. A particle in the harmonic oscillator potential has the initial wave function Psi(x, 0) = A[\psi_{0}(x) + \psi_{1}(x)] for some constant A. Here to and ₁ are the normalized ground state and the first excited state wavefunctions of the harmonic oscill
At t=0, a particle in a 1-D potential is described by the following wavefunction:
Prove that a unitary transformation can diagonalize a Hamiltonian
A particle of mass m and energy E moving along the x axis is subjected to a potential energy function U(x).
) A particle of mass m and energy E moving along the x axis is subjected to a potential energy function U(x).
) A particle of mass m and energy E moving along the x axis is subjected to a potential energy function U(x).
) A particle of mass m and energy E moving along the x axis is subjected to a potential energy function U(x).
The one-dimensional infinite potential well can be generalized to three dimensions.
The radial wave function for a hydrogen atom in the 3d state is given by
The normalized wave function for a hydrogen atom in the 2s state is
The wave function for a hydrogen atom in the ground state is given by
Consider a particle of total angular momentum j =1.
In class, we considered a box with walls at x = 0 and x = L. Now consider a box with width L but centered at x = 0, so that it extends from x = L/2 to x = L/2 as shown in the figure.
Consider a potential well defined as U(x) = for x < 0, U(x) = 0 for 0 < x < L, and U(x) = U0 > 0 for x > L (see the following figure).
A particle moving in one dimension is described by the wave function ...
Determine the energy of the particle if the proposed wave function satisfies the Schrödinger equation for x < 0.
Determine the function \psi(x).
Determine the constant N in terms of a
Calculate the minimum possible value of the energy E, and the value of x that gives this minimum E.
Question Regarding Selection Rules in Quantum Mechanics
Normalization find a constant c
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