Classical Mechanics
State Newton's Three Laws
1) An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force.
2) F=dp/dt
3) Whenever one object exerts a force on another object, the second object exerts an equal and opposite on the first.
The speed at which an electromagnetic wave travels in a vacuum
delta x delta p >= hbar/2
1) Energy cannot be created or destroyed
2) Entropy of the universe always increasesThis model described the atom as a ball of positive charge with negative charges embedded in it
plum pudding model
In what direction does the angular velocity vector point
Along the axis of rotation
Give an expression for the speed of light in terms of electromagnetic constants
c=1/sqrt(epsilon_0 * mu_0)
What is the difference between a fermion and a boson
Fermions have half integer spin, bosons have integer spin
What does thermal equilibrium mean in terms of entropy
State the parallel axis theorem
Iparallel = Icom + Md^2 where d is the distance between the axes and M is the mass of the rotating body
How do you find the magnetic field inside a toroid (be somewhat specific)
What is the commutator of the x and p operator
[x,p]=i hbar
Match the situation with the type of ensemble we use to describe it
1) Particles are isolated from the environment
2) Energy and number of particles allowed to be exchanged with the environment
3) Energy can be exchanged with the environment (but particle number fixed)
1) Microcanonical
2) Grand Canonical
3) Canonical
Discoverer of the nucleus and the name of the experiment conducted to discover it
Rutherford, gold-foil experiment
State Hamilton's equations of motion
dp/dt = - partial H/partial q
State all 4 maxwells equations, in their full glory, in differential form
Consider a spin 1/2 particle initialized in the state ket(psi)=sqrt(3)/2 ket(up) - 1/2 ket(down). ket(psi) is the state vector, ket(up) is spin up state and ket(down) is spin down state. What is the probability of measuring the particle in the spin up state and what is the probability of measuring the particle in the spin down state?
Spin up: 75%
Spin down: 25%This is the energy difference between the highest and lowest occupied state of non-interacting fermions at absolute zero.
Where was the cyclotron invented (which university)
UC Berkeley
Suppose you are moving near the speed of light with a clock relative to a stationary observer with a clock. 2 questions: Will your clock run faster or slower than the stationary clock, and by what factor will it be different (name or formula acceptable).
Your clock runs slower than the stationary clock. The factor it changes by is called the Lorenz factor.
Which gauge condition is used in non-relativistic E&M and which one is used in relativistic E&M (name or equation acceptable)
Non-relativistic: Coulomb gauge
Relativistic: Lorenz gauge
How do the ladder operators for the quantum harmonic oscillator act on a generic fock state ket(n)
a ket(n) = sqrt(n) ket(n-1)
a^dagger ket(n) = sqrt(n+1) ket(n+1)
a is lowering operator, a^dagger is raising operator
Given the total entropy associated with the randomized sequence of
DNA in a human is 9*10^(22) *k_b Joules/Kelvin. Given a cookie has 100 Calories, and body temperature is 310 K. How many cookies do we need to repair human’s DNA if it starts in a completely scrambled state? k_b is Boltzman's factor.
Approximately 10^(-4) cookies
When was Einsteins miracle year
1905