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L7 - Properties of stationary states • Spacing between...

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Wave Mechanics Erwin Schroedinger: an electron exhibiting wave-like properties can be described by a mathematical equation called wave equation. The electron is then described by a wave-function ( ψ ) corresponding to a standing wave, within the boundary conditions of the system under investigation. Ψ  e
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Probability of Finding a particle What is the physical meaning of a wavefunction ? •Wavefunctions are a useful mathematical concept. •The square modulus of a wavefunction (always non negative) does have a physical meaning it represents the probability density Max Born Particle most likely to be found in the center of the box a a
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What have we learned so far?
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How do we determine the constant B? Particle can ʼ t escape and must be somewhere in the box!
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Unformatted text preview: Properties of stationary states • Spacing between energy levels increases as n increases • Spacing increases as box size a decreases Properties of stationary states: sinusoidal waves Expectation values or average values Measure a certain quantity and record probability of getting a certain value “x” Probability of Fnding a particle Probability of Fnding a particle Particle most likely to be found in the center of the box a Integration by part Integration by part The rule is: Integration by part : Example (1.) Integration by part : Example (2.) Integration by part : Example (3.) Integration by part : Example (4.) Integration by part : Example (5.) Integration by part : Example (5.) Where do damped oscillations come from ?...
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