Phy107Spr06Lect26

Phy107Spr06Lect26 - From Last Time Course essay reference...

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1 Wed. Mar. 29, 2006 Phys107 Lecture 26 1 • Wednesday, Nov. 16, due in class – Reference to main article – Outline of essay. • Essay is 500-750 words (about 2 double-spaced typed pages) • So outline should be by paragraph • E.g. – I. Intro: (one-sentence summary) – II. Background/history (specific ‘high points’) – III. Specific example (identify the example) – etc Wed. Mar. 29, 2006 Phys107 Lecture 26 2 From Last Time… • Heisenberg Uncertainty principle • Arises from wave nature of particles. • Particle cannot have precise position and momentum. • Highly accurate momentum (wavelength) means position is uncertain • Can localize particle by superimposing many wavelengths, so momentum is uncertain. • Quantum mechanical tunneling. Wed. Mar. 29, 2006 Phys107 Lecture 26 3 More unusual aspects of quantum mechanics Quantum jumps : wavefunction of particle changes throughout all space when it changes quantum state. Superposition : quantum mechanics says wavefunction can be in two very different configurations, both at the same time. Entanglement : two quantum-mechanical objects can be intertwined so that their behaviors are instantly correlated over enormous distances. Wed. Mar. 29, 2006 Phys107 Lecture 26 4 The wavefunction and quantum ‘jumps’ • A quantum system has only certain discrete quantum states in which it can exist. • Each quantum state has distinct wavefunction, which extends throughout all space • It’s square gives probability of finding electron at a particular spatial location. • When particle changes it’s quantum state, wavefunction throughout all space changes. Wed. Mar. 29, 2006 Phys107 Lecture 26 5 Hydrogen atom quantum jump n =1 n =2 n =3 n =4 Wavefunction changes from 3 p to 1 s throughout all space. Photon emitted hf = E 3 -E 1 Wed. Mar. 29, 2006 Phys107 Lecture 26 6 The electron jumps from one quantum state to another, changing its wavefunction everywhere. During the transition, we say that the electron is in a superposition between the two states.
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2 Wed. Mar. 29, 2006 Phys107 Lecture 26 7 Classical particle in a box • Box is stationary, so average speed is zero. • But remember the classical version • Particle bounces back and forth. – On average, velocity is zero. – But not instantaneously – Sometimes velocity is to left, sometimes to right L Wed. Mar. 29, 2006 Phys107 Lecture 26 8 Quantum version • Quantum state is both velocities at the same time • Ground state is a standing wave, made equally of – Wave traveling right ( positive momentum + h / λ ) – Wave traveling left ( negative momentum - h / λ ) " = 2 L One half- wavelength p = h = h 2 L momentum L Quantum ground state is equal superposition of two very different motions. Wed. Mar. 29, 2006
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Phy107Spr06Lect26 - From Last Time Course essay reference...

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