An electron moving in a box of length ‘a’. If Z1 is the wave function at x1 = a/4 with n=1 and Z2 at x = a/4 for n=2 find Z1/Z2
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An electron moving in a box of length ‘a’. If Z1 is the wave function at x1 = a/4 with n=1 and Z2 at x = a/4 for n=2 find Z1/Z2
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- Calculate the uncertainties dr = V(x2) and op = V(p²) for %3D a particle confined in the region -a a, r<-a. %3DThe wave function W(x,t)=Ax^4 where A is a constant. If the particle in the box W is normalized. W(x)=Ax^4 (A x squared), for 0<=x<=1, and W(x) = 0 anywhere. A is a constant. Calculate the probability of getting a particle for the range x1 = 0 to x2 = 1/3 a. 1 × 10^-5 b. 2 × 10^-5 c. 3 × 10^-5 d. 4 × 10^-5Given a Gaussian wave function: Y(x) = (1/a)-1/4e-ax²/2 Where a is a positive constant 1) Find the normalization (if the wave function is not normalized) 2) Determine the mean value of the position x of the particle : x 3) Determine the mean value of x? : x? 4) Determine the value of Ax = /(x²) – (x)²
- The expectation value of a function f(x), denoted by (f(x)), is given by (f(x)) = f(x)\(x)|³dx +00 Yn(x) = where (x) is the normalised wave function. A one-dimensional box is on the x-axis in the region of 0 ≤ x ≤ L. The normalised wave functions for a particle in the box are given by -sin -8 Calculate (x) and (x²) for a particle in the nth state. n = 1, 2, 3, ....QUESTION 7 Use the Schrödinger equation to calculate the energy of a 1-dimensional particle-in-a-box system in which the normalized wave function is 4' = e sin(6x). The box boundaries are at x=0 and x=r/3. The potential energy is zero when 0 < x <- and o outside of these boundaries. 18h? m h2 8m h2 36n2m none are correctQUESTION 6 Consider a 1-dimensional particle-in-a-box system. How long is the box in radians if the wave function is Y =sin(8x) ? 4 4л none are correct T/2 O O O