Quantum Oscillator Problem Assignment Example | Topics and Well Written Essays - 250 words

Quantum Oscillator Problem - Assignment ExampleFigure 6.11 shows a plot of the tenth excite state probability density, 102. Mathematica has the Hermite polynomials built-in. The quantum oscillator wave functions are given in equation 6.57 these wave functions are not normalized. The in these equations is (HW Problem 6.36 and in-class work). The argument of the Hermite polynomials in equation 6.57 is listed as x but you allow for want to use = as the argument when you are actually write down or program the Hermite polynomials. (a)Write down the (un-normalized) wave function for the 10th excited state you can write it in terms of . Also write down the energy for this state (write this energy in terms and )? This fibre of which energy act on the energy eigenstates of the harmonic oscillator potential producing a un-normalized state of higher or lower energy. a =1/2m(/i/x imx)A=- 2 d2/2mr2d(b) Plot 10 and 102(use u rather than x for your independent variable) your 102 plot sho uld look like Figure 6.11. (c) Normalize 10 (use u) Normalization the stationary wave functions are r a 1 2 2 n (x) = 2n n Hn (ax) e a x 2 .The diodes are available in the normalized E24 1 % (BZX84-A), 2 % (BZX84-B) and approximately 5 % (BZX84-C) tolerance range. The serial includes 37 breakdown voltages with nominal working voltages from 2.4Vto75 V.(d) Find the probability that the electron is in the region 0.5 0.5. Use 3 significant figures for these numerical answers. (e) What is 2 for this excited state?