Show that the bound state wave function of the δ function's well is well orthogonal to...

Show that the bound state wave function of the δ function's well is well orthogonal to all scattering state wave functions.

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genius_generous answered 2 years ago

1).a) Show that the bound state wave function ψb (Eqn 2.129) and the continuum state wave...

1).a) Show that the bound state wave function ψb (Eqn 2.129) and the continuum state wave function ψk (Eqn 2.131-132 with coefficients 2.136-137) are orthogonal, i.e., 〈ψb|ψk〉 = 0. (b) [bonus] Explain why the orthogonality exists, example as, are they eigenstates of an operator? If so, what is the operator? If not explain.

Show how the wave function of the even states of a particle in an infinite well...

Show how the wave function of the even states of a particle in an infinite well extending from x=-L/2 to x=L/2 evolve in time. Details!

Show that the deuteron has no bound excited states by estimating the excited state energy and...

Show that the deuteron has no bound excited states by estimating the excited state energy and comparing it to the potential well. Consider two cases for the excited state: a) higher order radial eigenfunctions, b) non-zero angular momentum. c) If the nuclear force had a longer range R >R0 we could possibly have excited states. What would be the minimum and maximum values of R∗ so that there could be an excited state with l = 1 but no excited...

Show that the eigenfunctions un(x) are orthogonal .

An electron is bound to a finite potential well. (a) If the width of the well...

An electron is bound to a finite potential well. (a) If the width of the well is 4 a.u., determine numerically the minimum depth (in a.u.) such that there are four even states. Give the energies of all states including odd ones to at least 3 digits. (b) Repeat the calculation, but now keep the depth of the well at 1 a.u., determine the minimum width (in a.u.)

(2) Please show that a discontinuity arises in the first derivative of the wave function of...

(2) Please show that a discontinuity arises in the first derivative of the wave function of the infinite potential well (0 to L).

Consider two electrons, both in the ground state of an in?nite potential well. Write the wave...

Consider two electrons, both in the ground state of an in?nite potential well. Write the wave function ?(x1,x2) for this system. Assume the electrons are non-interacting

In 1-D, the finite square well always has at least one bound state, no matter how...

In 1-D, the finite square well always has at least one bound state, no matter how shallow the well is. In 3-D, a finite-depth well doesn't always have a bound state.find bound states

An atom is in a time independent one-dimensional potential well. The system's spatial wave function at...

An atom is in a time independent one-dimensional potential well. The system's spatial wave function at t=0 is Ψ(x,0) = Ax(a-x) for 0<x<a and zero for all other x. (a) The system's energy is measured at t=0. What is the most likely outcome? Find the probability for obtaining this result. (b) What is the systems's average energy at t=0? Compare it with the energy in (a) and explain your answer.

Sketch the wave-function of the ground state of a particle of mass m which is con-...

Sketch the wave-function of the ground state of a particle of mass m which is con- fined in one dimension within a square potential well of infinite height, centred at x = 0 and of width a between x = ?a/2 and x = a/2. What type of function is that? If the infinite potential well is replaced by a potential well of finite height, sketch the new ground state wave-function. Explain qualitatively how the ground state energy changes in...

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