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Unformatted text preview: Physics 3316, Spring 2010 Basics of Quantum Mechanics Study Guide for Prelim 1 This study guide contains a brief outline of the material covered in class thus far. The initial discussion in class focused on various experimental discoveries that pointed to the fact that classical mechanics was incomplete. In particular, our classical intuition that matter/energy can be clearly identified as either particle- like entities or wave-like entities, and that particulate matter can be assigned a well defined trajectory in phase space no longer holds in the quantum world. The following gives a quick summary of the seminal experiments that led to these insights. Students should be comfortable with the basic conclusions of these experiments. Quantum Theory: a fundamental description of the behavior of matter and energy 1. Experiments establishing the identity/nature of the building blocks of the microscopic world (a) Nuclei — Rutherford Scattering (b) Electrons ( E = radicalbig ( cp ) 2 + ( mc 2 ) 2 + V ) i. J.J. Thomson’s, E × B experiment ⇒ measure e/m ii. R.A. Millikan’s oil drop experiment ⇒ measure e iii. Davisson-Germer/G.P. Thomson Experiments ⇒ wave-like nature of electrons with λ = h/p iv. Classical mechanics ( ⇒ v = ∂E/∂p ) + correspondence principle ( ⇒ c g = v ) leads to the De Broglie Hypotheses, p = h/λ and E = hν . From this argument we see why both the energy- frequency and the wavelength-momentum h ’s are the same and why the h ’s are the same for all objects. v. Double-slit thought-experiments ( ⇒ interference patterns) + the discreteness of microscopic events leads to the idea that microscopic events are probabilistic in nature but with a predictable distribution. We find that the probability of an event P = | Ψ | 2 is the complex magnitude squared of a wave-like amplitude. The amplitude function Ψ somehow senses and propagates through the entire...
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- Spring '08
- mechanics, Simple Harmonic Oscillator, Quantum state, Correspondence principle, quantum states, pure quantum state