Part B and C please! 1-D Schrödinger's equation(a) Re-derive the solution of Schrödinger's 1-dimensional equation for a particlein a box making sure you understand each step. What's the minimum energyof the wave-particle?(b) What's the average position of the wave-particle for each stationary state?(c) What's the variance of the position of the wave-particle for each stationarystate? What's the value when the energy level becomes very large compared tothe minimum energy?context and insightful tips(1) A possible sequence for the steps is: Start from the 1-dimensional equation,apply separation of variables, justify the choice of the constants, apply boundaryconditions, normalize the wave functions and identify the energy levels.Yn Yr, n(2) Recall that pn =1,2,... is the probability density associated withthe stationary state n(x, t). First of all you'll notice that pn does not dependon time (although n does). Then, you may use the standard definition of theaverage value of a random variable given its probability density function to findthe answer:=n=(10)Notice that pn is non-zero in a finite interval of x only, so the previous integralgets reduced to only that region. Moreover, you may find useful these two well-known results from calculus:[xpn(x) dx.·∞2sin ax =]Hint: is the same for all n.x cos ax dx1 - cos 2ax2x sin axa+cos axa²(11)(12)

Given:The wavefunction of Particle in a 1-D box of length L:To find:a) Expectation value of the position of a particle trapped in the 1-D box.b) Variance of the position of particle for each stationary stateStep 2:a) Expectation value of the position of a particle trapped in the 1-D box.We know, The normalized wavefunction of a Particle in a 1-D box of length L: & Therefore, The expectation value for the position is defined as :This is because a particle trapped in a 1-D box will have a non-zero wavefunction inside the box that is within 0 to L, and the wavefunction will be zero outside the box.Thus, the expectation or the average value of the particle in a 1-D box in the ground state or excited state or any stationary state will be L/2b) Variance of the position of particle for each stationary stateWe know, (Variance) = We need to know Thus, The variance for each stationary state is given by,When the energy level becomes very large that means the value of n tends to infinity then the variance will beHence we got the required expressions.

Answered: (b) What's the average position of the…

(b) What's the average position of the wave-particle for each stationary state? (c) What's the variance of the position of the wave-particle for each stationary state? What's the value when the energy level becomes very large compared to the minimum energy?