Flashcards
Quantum Equations (2)
Cards in this deck (13)
- 1—Energy-time version of the uncertainty principle for gaussian wave packets.
- 2—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.
- 3—This is the equation for the group velocity (it's like the velocity of a wave packet). Ugr is also equal to dw/dk
- 4—Uncertainty principle for a gaussian wave packet in terms of momentum and position.
- 5—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.
- 6—This is probability density. It represents the probability of finding a particle in a given volume at a given instant of time.
- 7—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.
- 8—Time dilation! Moving clocks run slower. Here's length contraction as well. Moving lengths contract.
- 9—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.
- 10—We can preserve conservation of linear momentum through a modification of the definition of linear momentum. u is the velocity.
- 11—Relativistic Kinetic Energy! It converges to 1/2mv^2 at low energies.
- 12—This is the total energy of a particle. E(0) is the rest energy, K is kinetic.
- 13—This is conservation of mass-energy. It shows that energy of a photon = pc.
