Quantum Equations (2)

megangoodland
Flashcards by megangoodland, updated more than 1 year ago
megangoodland
Created by megangoodland about 5 years ago
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Energy-time version of the uncertainty principle for gaussian wave packets.
This is the equation for a gaussian wave packet when time=0. The exponential part is the envelope, and the cosine part is the wave oscillating inside the envelope.
This is the equation for the group velocity (it's like the velocity of a wave packet). Ugr is also equal to dw/dk
Uncertainty principle for a gaussian wave packet in terms of momentum and position.
Minimum kinetic energy of a particle in a one dimensional box of length l. This comes with the assumption that the minimum value for the momentum is at least as large as its uncertainty.
This is probability density. It represents the probability of finding a particle in a given volume at a given instant of time.
Using Einstein's postulates, a transformation can be found between K and K' (which is travelling along x and x'). Gamma is the relativistic factor (=1 when v=0), which we worry about when it gets around 1.005.
Time dilation! Moving clocks run slower. Here's length contraction as well. Moving lengths contract.
Doppler Effect for light. Beta = v/c still, and it's positive when the source and receiver are getting closer, negative when they're moving farther apart.
We can preserve conservation of linear momentum through a modification of the definition of linear momentum. u is the velocity.
Relativistic Kinetic Energy! It converges to 1/2mv^2 at low energies.
This is the total energy of a particle. E(0) is the rest energy, K is kinetic.
This is conservation of mass-energy. It shows that energy of a photon = pc.
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