1. Given the wave function (a) Find N to normalize (x). (x)= = N x² + a²
Q: 1. A particle of m moves in the attractive central potential: V(r) = ax6, where a is a constant and…
A: Ans 1: (a) A=(π2b)1/4. (b) E(b)=2mbℏ2+64b315α. (c) bmin=(32ℏ245αm)1/4. (d)…
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Q: 1. Consider the n = 3 mode of the infinite square well potential with width L. (a) Draw the…
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Q: 3. In the potential barrier problem, if the barrier is from x-aa, E a region? (k²: 2mE > 0) ħ² Ans:
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Q: Given a Gaussian wave function: Y(x) = e-mwx?/h %D Where a is a positive constant 1) Find the…
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Q: 9. Estimate the ground-state energy of a harmonic oscillator using the following trial wavefunction.…
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Q: Discuss the general properties of the eigenstates of the quantum harmonic oscillator.
A: The normalized wave function for the harmonic oscillator is given as, ψnx=mωh2nn!π12e-mωhx2Hnmωhx…
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Q: Q1: Find the first excited state of harmonic oscillator using the equation: ₂(x) = A (a*)(x). with…
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Q: 2. For the following 4 cases, set up the correct integral to find the expectation values, for…
A: In this question, all four questions are different and are not inter-related to each other. For…
Q: 1. For the n 4 state of the finite square well potential, sketch: (a) the wave function (b) the…
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Q: 2. Consider a density operator p. Show that tr (p²) < 1 with tr (p²) = 1 if and only if p is a pure…
A: Introduction: Consider an ensemble of given objects in the states. If all the objects are in the…
Q: 1. Use the I function to do the following: TZ (a) prove that z!(-z)! where z is any real number .…
A: Using the Gauss representation of the Gamma function:…
Q: 1. A particle of m moves in the attractive central potential: V(r) = ax6, where a is a constant and…
A: The objective of the question is to compute the normalization constant A, calculate the ground state…
Q: 1. Given the following probability density function: p(x) = Ae-A(x-a)². %3D 2. A particle of mass,…
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Q: 2. A particle is confined to the x-axis between x = 0 and x = 3a. The wave function of the particle…
A: The detailed solution is following.
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- 4 (X) = Ne-a lxl Normalize the function (Step by step)16. Consider the wave function Mx) = (alT)" exp(-ax12) Calculate (x) for n = 1, 2. Can you quickly write down the result for (")?4) Consider the one-dimensional wave function given below. (a) Draw a graph of the wave function for the region defined. (b) Determine the value of the normalization constant. (c) What is the probability of finding the particle between x = o and x = a? (d) Show that the wave function is a solution of the non-relativistic wave equation (Schrodinger equation) for a constant potential. (e) What is the energy of the wave function? (x) = A exp(-x/a) for x > o (x) = A exp(+x/a) for x < o
- QUESTION 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 O24. Consider a modified box potential with V(x) = V₁x, Vi(ar), x a Use the orthogonal trial function = c₁f₁+c₂f₂ with f₁ = √√sin (H) and f2 = √√ √√sin sin (2) to determine the upper bound to ground state energy.