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in solving the schrodinger equation for the particle in a box system, satisfying the boundary condition imposes:
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- The general solution of the Schrodinger equation for a particle confined in an infinite square-well potential (where V = 0) of width L is w(x)= C sin kx + Dcos kx V2mE k where C and D are constants, E is the energy of the particle and m is the mass of the particle. Show that the energy E of the particle inside the square-well potential is quantised.Write down the Schrödinger equation for this PITB system.Calculate the reflection probability of a particle with a kinetic energy of Ekin = 4 eV at a negative potential step of height Eo = -12 eV starting from the time-independent Schrödinger equation.
- Solve the time-independent Schrödinger equation and determine the energy levels and the wave function of a particle in the potential a? V (x) = Vol a + 2r2 with a = const.Prove that this is a solution to the Schroedinger time-independent equationUsing the wave function and energy E, apply the Schrodinger equation for the particle within the box.
- A neutron of mass m of energy E a,V(x) = Vo ) II. Estimate the kinetic energy of the neutron when they reach region III.consider an infinite square well with sides at x= -L/2 and x = L/2 (centered at the origin). Then the potential energy is 0 for [x] L/2 Let E be the total energy of the particle. =0 (a) Solve the one-dimensional time-independent Schrodinger equation to find y(x) in each region. (b) Apply the boundary condition that must be continuous. (c) Apply the normalization condition. (d) Find the allowed values of E. (e) Sketch w(x) for the three lowest energy states. (f) Compare your results for (d) and (e) to the infinite square well (with sides at x=0 and x=L)Work out the Schrodinger equation (explain in detail with calculations) using energy conservation.
- Given a particle is confined to a 1D infinite potential well from -a/2 < x < a/2, prove that the wavefunction solution to the Schrodinger equation has form: XTU α = Bcos (2n + 1) 1) Pn(x) = inside the potential well, where n is any integer.Solve the Schrodinger equation for a quantum particle of massm trapped in a one-dimensional infinite potential well (box) oflength L and obtain the expressions for wave-functions of theparticle.For a particle of V(x) = KX, mass m X>0 moving in a potential = 8 › X <0 where K is a constant optimize the wavefunction = x exp{-ax}, where a is the variable parameter. of the system using Find the ground stade energy time independent schrodinger equation