A particle is confined in an one dimensional box (0<x<L). The probability of finding the particle in the interval 0<x<L isa.1b.depends on the quantum number nc.depends on the energy of the particle

A particle is confined in a 1D box (0<x<L). The ratio of the energies of the particle in state n=3 to state n=2 isa.9/4b.1/4c.4

Evaluate the probability that a particle trapped in a box L wide can be found between 0.45L and 0.55L for the ground and first excited states.

Boundary conditions and normalization determine the wave functions. Considering a particle trapped in a box with infinitely hard walls, comment on the above sentence and find wave function nthat corresponds to various energy levels. Where is this particle most likely to be in the lowest energy level and what will be the probability of finding the particle at this location in the next higher energy state?

6.Question 6Suppose we have a particle in 1-dimension, with wavefunction 𝐴𝑒−∣𝑥∣2𝑑Ae − 2d∣x∣​ .What is the probability to find the particle in the interval [0,𝑑][0,d]?Please provide your answer in terms of 𝐴A, 𝑑d, mathematical constants such as 𝜋π (entered as 1pi) or 𝑒e (entered as 1e).(Assume that A is real)1 point0.5*(1-e^-1)A^2*d*(1-exp(-1))A^2*d*(1-e^-1)0.5*(1-exp(-1))

A particle in a one dimensional infinite square well (box) is in a superposition of two quantum states:1 21234   where1 2and  are orthogonal, normalized (ortho-normal) eigenfunctions of the Hamiltonian.(a) Calculate the new normalization constants for1 2and  . [2 marks](b) A measurement of energy is made. What is the probability that the measurement will find energy1E ?What is the probability that the measurement will find energy2E ? [2 marks](c) Write down the integral expression for the evaluation of the expectation value of position,x - evaluateany “trivial” integrals, but leave as integrals any that require a full solution. [2 marks](d) Write down the integral expression for the evaluation of the expectation value of momentum,xp -evaluate any “trivial” integrals, but leave as integrals any that require a full solution