1 Consider an electron in the spin-state σ = √2 =[α + B]. (a) Is σ an eigenfunction of Ŝ²? If yes, what is the eigenvalue and what is the corresponding spin magnitude? If no, what is the expectation value? (b) Is σ an eigenfunction of Ŝ, ? If yes, what is the eigenvalue? If no, what is the expectation value?
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- TRQ. 3 Solve completely the following Quantum problem. Need full detailed answer, equations and if possible, theory/ literature. Question: A particle of spin 1 and a particle of spin 1/2 are in a configuration for which the total spin is equal to 1/2. If one were to measure the z-component of the spin of the particle with spin=1, what values might one get and what are the probabilities associated with those values?TRQ. 3.1 Solve completely the following Quantum problem. Need full detailed answer, equations and if possible, theory/ literature. Question: A particle of spin 1 and a particle of spin 1/2 are in a configuration for which the total spin is equal to 1/2. If one were to measure the z-component of the spin of the particle with spin = 1, what values might one get and what are the probabilities associated with those values? Use Clebsch-Gordan table. Write the total spin state |s,ms> as linear combinations of |s1, ms1> |s2, ms2> states.Sketch the potential energy function of an electron in a hydrogen atom, (a) What is the value of this function at r=0 ? in the limit that r=? (b) What is unreasonable or inconsistent with the former result?
- Problem 1. Two State System Consider an atom with only two states: a ground state with energy 0, and an excited state with energy A. Determine the mean energy (e) and variance in energy (de). Sketch the mean energy versus A/k T.I1 This time, let us consider a maxed spin state in which the electrons have equal probabilities of being in the pure states 8x+) and sy+)..What is the energy level difference between adjacent levels ∆En = En +1 - En for the simple harmonic oscillator? What are ∆E0, ∆E2, and ∆E20? How many possible energy levels are there?
- Physics Department PHYS4101 (Quantum Mechanics) Assignment 2 (Fall 2020) Name & ID#. A three-dimensional harmonic oscillator of mass m has the potential energy 1 1 1 V(x.y.2) = ; mw*x² +mwży² +=mw;z? where w1 = 2w a. Write its general eigenvalues and eigenfunctions b. Determine the eigenvalues and their degeneracies up to the 4th excited state c. The oscillator is initially equally likely found in the ground, first and second excited states and is also equally likely found among the states of the degenerate levels. Calculate the expectation values of the product xyz at time t2. Consider the quantum state vector = √ + x - √√₁ - x ->x. a. What are the possible measurements of the spin component S₂ and with what probabilities will they occur? b. What are the possible measurements of the spin component Sy and with what probabilities will they occur?Chapter 39, Problem 015 An electron is trapped in a one-dimensional infinite potential well that is 150 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width dx = 5.0 pm centered at x = 56 pm? (Hint: The interval dx is so narrow that you can take the probability density to be constant within it.) Number Units
- Consider a three-dimensional infinite potential well with a quantized energy of Enn,n, %3D (n + ng + n). where n = 1,2,3, ..,n, = 1,2,3, .., n, = 1,2,3, and a represents the 2ma potential well width in the x, y, and z directions. i. The lowest energy level that the electron may occupy is ii. The values of (ng, ny, ng) for the next higher energy level that is above the lowest energy level can be iii. If the electron drops from the energy level in item (ii) to the energy level in item (i), what is the wavelength of a photon that may be emitted if the work function is 0.4 V? Assume a=0.1 iv. Let the wave function has the general form Y(x,y, z) Asin nyy sin sin The value of A would be, v. Let (n, = 2, n, = 2,n, = 2). What is the probability that an electron exists in the intervals Osxs 0sys and o s z s?Starting from the N(p) expression of a 3D conductor, derive an expression for the exact density of states D(E) for the 3D conductor in the below graph (You have to show all the steps that lead to your final answer). The length of the conductor is given as L = 20 nm and the diameter is given as D= 4 nm. The +E.. 2mo energy momentum relationship is given as: E =The energy eigenvalues of a 3-dimensional infinite well of sides a, b, c is given by Enml (n2 + m² +P)Eo Here n, m, lequal to 1, 2, .and E, is a constant energy. If b= a, c = 4, the energy levels up to the fourth excited state level in terms of En are Select one: O a. 4, 6, 13, 14 O b. 3, 6, 9, 11, 12 C. 4, 6, 9, 11, 12 O d. 4, 7, 10, 12, 13 О е. 4, 7, 9, 13, 14