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))

The wave function for a quantum particle is given byψ(x)=Aexp(−|x|a) where A and a = 1 are constants and −∞ < x < +∞.Hint: It will be useful to break any integration into 2 parts.Find the value of the normalisation constant A.Answer for part 1 Find the probability that the particle will be found in the interval −a < x < a.

The wave function for a quantum particle is given by𝜓(x)= Axbetween x = 0 and x = 1.00, and 𝜓(x) = 0 elsewhere.Find the value of the normalisation constant A.Answer for part 1 Find the expectation value of the particle's position.Answer for part 2Find the probability that the particle will be found between x = 0.245 and x = 0.465.

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

Question 7What is the probability current density of a particle with wavefunction 𝜓(𝑥,𝑡)=exp⁡(𝑖ℏ(𝑝𝑥−𝐸𝑡))ψ(x,t)=exp( ℏi​ (px−Et))?Recall that the probability current density can be computed as:𝑗=ℏ2𝑚𝑖[𝜓∗∂∂𝑥𝜓−𝜓∂∂𝑥𝜓∗]j= 2miℏ​ [ψ ∗ ∂x∂​ ψ−ψ ∂x∂​ ψ ∗ ]1 point𝑝𝐸Ep​ 11𝑝p𝑝𝑚mp​

A particle in a central potential V (r) has a wavefunction of Ψ= f (r,Ө) sin2Ø where Ø is the azimuthal angle in the spherical polar coordinate system. Also, this wavefunction Ψ is properly normalized, i.e.˂ΨӏΨ˃=1Read the following passage to answer the given questions based on it. Choose the correct options. (Marks: 1)What is the probability of measuring L+OPTIONS 0 1 0.01 0.1