Lect38_[Compatibility_Mode] (1)

# Lect38_[Compatibility_Mode] (1) - Physics 344 Foundations...

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Physics 344 Foundations of 21 st Century Physics: Relativity, Quantum Mechanics and heir Applications Their Applications Instructor: Dr. Mark Haugan Office: PHYS 282 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Shuo Liu Office: PHYS 283 [email protected] Office Hours: If you have questions, just email us to make an ppointment. e enjoy talking about physics! appointment. We enjoy talking about physics! Reading: Six Ideas Unit Q, Chapters 5 through 11 Notices: Final Exam Tuesday, December 14 7:00pm in MSEE B012

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Question 1. If we model an electron bound in an F-center as an electron in a box a = 0.2 nm on a side, estimate the kinetic energy of the electron in the system’s ground state? int: You don’t need to remember the formula for the answer Recall what ( ) ( ) ( ) ( , , ) sin sin sin nlm x y z x y zk x k x k x ψ Hint: You don t need to remember the formula for the answer. Recall what the system’s wavefunction must look like and use fundamental things that you know. Recall that in MKS units h = 6.6e-34 Æ ħ =1.05e-34 ) 1.5e- 8 J ) 1.5e- 9 J that mass of an electron is m = 9e-31 kg that wavevector and wavelength are related by k = 2 π / λ A) 1.5e 18 J B) 1.5e 19 J *C) 4.5e-18 J D) 4.6e-19 J Relationship of this question to to a Midterm II test question
article Spin Particle Spin Last time we briefly discussed the energy eigenstates of an electron in a (perfectly conducting) circular wire loop and showed that these could also be eigenstates z-component (perpendicular to the wire loop’s plane) of angular g p( p p p p ) g momentum. In addition, the magnetic moment of the electron-wire system would be quantized. In that case, demanding that the time-independent Schrödinger equation be a case, de a d g a e e depe de Sc öd ge equa o be satisfied everywhere within the wire loop lead to L z eigenvalues n ħ where n is a non-negative integer. When we discuss electrons moving in 3-d again next time, we’ll see that the same demand when, as in atoms, an electron is oving in a spherically symmetric potential such energy eigenvalues come moving in a spherically symmetric potential such energy eigenvalues come in sets with degeneracy 2 n + 1, corresponding to different values of L z with stepping up from – n ħ to n ħ . In other words, there is 1 state with L z = 0, there are 3 with L = ħ and so on. Today, we will finally discuss why it is that we say that electrons (and protons, neutrons and many other particles) have spin ½. his will give us one more opportunity to put all of the fundamental rules of z This will give us one more opportunity to put all of the fundamental rules of quantum mechanics through their paces.

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he Stern- erlach Experiment The Stern Gerlach Experiment A low-energy beam of electrons with well-defined momentum is directed through a region with a magnetic field oriented in the z direction. The
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## This note was uploaded on 03/23/2011 for the course PHYS 344 taught by Professor Garfinkel during the Fall '08 term at Purdue.

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Lect38_[Compatibility_Mode] (1) - Physics 344 Foundations...

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