Q2: Find the second excited state of a harmonic oscillator using the equation: 4,(x) = A,(a,)" 4,(x), with En = (n +)ħw

Q: 5. A free particle has the following wave function at t = 0: V(x,0) = Ne-a|x| = [Ne-ª* x>0 Near x <…

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Q: 32. Check the normalization of ψ0 and ψ1 for the harmonic oscillator and prove they are orthogonal.…

A: To find the normalization constant C0 and C1 and check the orthogonality of the two wavefuction

Q: 2. Prove, using the formal limit definition of the derivative, that if f(x) = then f'(2) = -1

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Q: 8-6. If you were to use a trial function of the form p(x) = (1+cax²)e-ax²/2, where a = (ku/h²)1/2…

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Q: 2) Consider a particle in a three-dimensional harmonic oscillator potential V (x, y, 2) = ;mw (x² +…

A: Let the given particle is the electron. Then the transition probability (W) be given as, Where, ω…

Q: 2. Find the best bound on Es for the one-dimensional harmonic oscillator using the trial wave…

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Q: Let f(x) = 4xe- sin(5x). Find the third derivative of this function. Note e* is denoted as e^x…

A: Derivative of two multiplicative function is given as  (fg)′=f′g+fg′

Q: 2 σE²: OE = (E²) - (E)² for a particle in a box in the state described by V(x) = √3(x) + 2√₁(x),…

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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: You are given a free particle (no potential) Hamiltonian Ĥ dependent wave-functions ¥₁(x, t) V₂(x,…

A: Given Data: The Hamiltonian of the particle is,  H=−ℏ22md2dx2.The two wavefunctions are…

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: 3. The ground state and first excited state of the SHO for angular frequency w are Yo (x) = a…

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Q: PROBLEM 1 Consider a ld oscillator subject to an additional constant force F, so that the potential…

A: Wavefunction obtained for a normal harmonic oscillator is, ψnx=12nn!mωπℏ14e-mωx22ℏHnmωℏx Energy is,…

Q: Which is the Schrodinger equation for a 1D harmonic oscillator:

A: The harmonic oscillator Hamiltonian is given by, H=p22m+12kx2 Here, m is the mass, k is the force…

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: -h? d? 3. Find average value of kinetic energy, for ground state of the harmonic 2µ dx? ocillator.…

A: We have to use some basic formula here

Q: 2) Consider a particle in a three-dimensional harmonic oscillator potential V (r, y, z) = 5mw²(r² +…

A: The energy for state Ψ201 can be defined as,