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### Phys301-11

Course: PHYSICS 301, Fall 2009
School: Idaho State
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Word Count: 529

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Physics Fall Modern 2008, Dr. Starovoitova Lecture 11 Review Lecture 10 Matter waves, De Broglie relations Electron diffraction Waves: , , T, and k Fourier series and Fourier integral 11.1. Uncertainty principle Electron in space: position, momentum, energy, time Heisenberg showed that no matter how accurate the instruments used, quantum mechanics limits the precision when two properties are measured at the...

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Physics Fall Modern 2008, Dr. Starovoitova Lecture 11 Review Lecture 10 Matter waves, De Broglie relations Electron diffraction Waves: , , T, and k Fourier series and Fourier integral 11.1. Uncertainty principle Electron in space: position, momentum, energy, time Heisenberg showed that no matter how accurate the instruments used, quantum mechanics limits the precision when two properties are measured at the same time. 1 kx 2 2 2 p = = k= h/ p h h px 2 11.1. Uncertainty principle 1 t 2 Many excited states are not stable and decay in about t=10-8 s. Thus E=3x10-8 eV E = hf = h = h 2 h tE 2 11.2. Heisenbergs microscope Heisenberg pictured a microscope that obtains very high resolution by using high-energy gamma rays for illumination. The microscope can resolve objects to a size of x, which is related to the wavelength of the gamma ray, by the expression: x = / (2sinA) Momentum before: p=h/ 1)Momentum after: p'x + (h sinA ) / ' 2)Momentum after: p''x - (h sinA ) / '' p'x + (h sinA ) / ' = p''x - (h sinA ) / '' p''x - p'x = px ~ 2h sinA / Since x ~ /(2sinA) and px ~ 2h sinA / , x px ~ h 11.3. Implications I believe that the existence of the classical "path" can be pregnantly formulated as follows: The "path" comes into existence only when we observe it. In the sharp formulation of the law of causality-- "if we know the present exactly, we can calculate the future"-it is not the conclusion that is wrong but the premise. Heisenberg, in uncertainty principle paper, 1927 11.4. Quantum wave function A wave function is a mathematical tool used in quantum mechanics to describe any physical system. It is a function a from space that maps the possible states of the system into the complex numbers. The laws of quantum mechanics describe how the wave function evolves over time. Quantum coral shows electron wave functions (sort of) 11.4. Quantum wave function F(t) m Classical Physics: Newtons 2nd Law r r a = F /m x(t ) Quantum Mechanics: Schrodinger Equation ( x, t ) 11.4. Quantum wave function Statistical interpretation: ( x, t ) dx 2 probability of finding the particle between x and x + dx = * 2 = 0.2i 0.5 * = 0.2i 0.5 2 Always real and positive! = (0.2i 0.5)(0.2i 0.5) = 0.04i 2 + 0.1i 0.1i + 0.025 = 0.065 11.5. Indeterminacy Suppose you measure the position of the particle and find it at point C. Question: Where was it right before the measurement? C 1) The realist position (at C) - Einstein 2) The orthodox position (wasnt really anywhere) - Bohr 3) The agnostic position (refuse to answer) - Pauli 11.5. Indeterminacy The position of the particle was never undeterminate, but wa...

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Idaho State - PHYSICS - 301
Modern PhysicsFall 2008, Dr. Starovoitova Lecture 9Review Lecture 8 Atomic spectra Balmer formula General formula Bohr atomER En = 2 n 2 r = n aB9.1. Properties of Bohr atomThe state of the lowest energy is called ground state:E1 = ER
Idaho State - PHYSICS - 301
Modern PhysicsFall 2008, Dr. Starovoitova Lecture 10Review Lecture 9 Properties of Bohr's atoms Hydrogen-like ions Mass correction Frank-Hertz experiment10.1. Matter WavesE = hf p= hDe Broglie relations are applied to matter waves.2r
Idaho State - PHYSICS - 301
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Idaho State - PHYSICS - 301
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Inverse Square LawWhen the light meter is 40 centimeters from the light, the light intensity is 0.41 (unit). What are the intensities at the double and triple distances, respectively? a.) 0.20 and 0.14. b.) 0.10 and 0.05. c.) 0.16 and 0.06. d.) 0.05
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