An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter A.4, Problem 23P
To determine
To Draw:The cone diagram for the spin states of a particle with
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For Problem 9.19, how do I manage to solve for part B? The title of this chapter is Electron Spin. This problem is part of quantum mechanics. Here is a page that may assist in what we're dealing with.
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+)..
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An Introduction to Thermal Physics
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- Consider a two-electron spin system in a singlet state. a. If a measurement of one of the electrons shows that it is in a state with sz = 1/2, what is the probability of obtaining another state with sz= +1/2? b. If a measurement of one of the electrons shows that it is in a state with sx = 1/2, what is the probability of obtaining another state with sy = +1/2?arrow_forwardProblem 4. Consider two indistinguishable, noninteracting spin-1/2 fermions in a one- dimensional infinite square well potential of length L. (a) What is the ground-state energy of the two-particle system? (b) What is the ground-state quantum state vector? (c) What is the first excited state energy of the two-particle system? (d) What are the quantum state vectors of the first excited state? (e) What is the degeneracy of the first excited state? (f) Discuss qualitatively how the excited-state energies change if we consider the particles to be interacting through the Coulomb potential.arrow_forwardA Construct the wavefunction V(r, 0, ¢) for an H atoms' electron in the state 2pz. Please note that in order to have a real-valued wavefunction of pr orbital(see below), you need to do a linear superposition of the corresponding spherical harmonics for the angular part. Use the spherical harmonics table below. Show that the superposition you selected indeed results in a real orbital; however, you do not need to simplify the expressions further or normalize the wavefunction. Px 1/2 Yg = ()"" (5 cos 0 -3 cos 0) cos e %3D (4x 21 12 64л/ 1/2 sin e (5 cos? e- 1)eti 87 -y Y = (3 cos²0 – 1) 105 1/2 32 sin e cos de2ie (167 15 12 sin e cos betie 35 12 (647 sin de i B Now consider an excited state of He atom with electron configuration 1s 2s'. In general, the wavefunction is a state: V(r, 0, 0, 02) = V(r,0, ø)V.. where V(r, 0, 6) and V,, represent the spatial and the spin part. The spatial part is constructed from the wavefunctions of the 1s' and 2s' orbitals denoted as o (r, 0, ø) and o (r, 0,…arrow_forward
- a) Explain how the alpha parameter in the general E(p) relation, and the channel dimension could be used to determine the density of states as function of the energy E. b) Provide and define the two main parameters (terms) that determine the electron density when temperature is non zero.arrow_forwardPart A Calculate the transition dipole moment, = / v. (r)H(r)dr where -er cos(e) tor a transition from the 1s level to the 4p, level in H. The integration is over r, 0, and o. Use 5 cos(e) 645 ao 2 a for the 4p, wave function, Use 3/2 the = for the la wave function. To solve this problem you may need to evaluate the following integral: Express your answer in coulomb-metera to three significant figures. C-m Submit Previous Answers Request Answerarrow_forwardThe valence election of potassium is excited to a 5d state, (a) What is the magnitude of the election's orbital angular momentum? (b) How many states are possible along a chosen direction?arrow_forward
- Consider hydrogen in the ground state, 100 . (a) Use the derivative to determine the radial position for which the probability density, P(r), is a maximum. (b) Use the integral concept to determine the average radial position. (This is called the expectation value of the electrons radial position.) Express your answers into terms of the Bohr radius, a0. Hint: The expectation value is the just average value, (c) Why are these values different?arrow_forward7c.2. Evaluate for the total energy & at the following k-directions and evaluate at the BZ boundary. a. (1,0,0) b. (1,1,0) c. (1,1,1)arrow_forwardsolve it completely. What are the additional assumption made in the shell model ? Discuss the possible cause for (a) the difference in the energy of j+1/2 and j-1/2 states (b) the pairing energy.arrow_forward
- 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?arrow_forwardA Lennard-Jones potential with repulsive interaction prep (r) = A.r-12 with A =58.68 eV Å12 and Patt (r) = -B.r- with B =0.16 eV ź. Derive the force distance curve and calculate the equilibrium distance. Give your results in Å and round if off to two decimal places, i.e. the nearest hundredth.arrow_forward: Derive a state space model for the system shown in Figure below when the input is fa and the output is z.arrow_forward
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