Quantum mechanics george notes Flashcards
what is quantum mechanics written in terms of
eigen equations
what does an eigen equation have
eigen functions, eigenvalue, and an operator
what is the general form of an eigen equation
operator (acts on ) eigen function = eigen value X eigen function
what is the position operator in 1D
X
What is the momentum operator
p^=-ih(bar)d/dx or p^=-iH(bar)GRAD
kinetic energy
T=p^2/2m
kinetic energy operator
T^=P^2/2m = -h(bar)/2m d^2/dx^2 = -h(bar/2m (GRAD^2)
what is Hamiltonian operator
the total energy operator
what is the eigen equation for the total energy
H^ x (wavefunction) = E x (wavefunction )
what is the expectation value
the expectation value of a system is the value you expect to get. position, momentum and energy have expectation value other variables do too.
what is degeneracy
when two different quantum states give the same value
what does the wavefunction collapsing mean
the wave function collapses when a measurement is performed. when you measure a property of the system you collapse the wavefunction from many possible states to one known state.
orthonormal equation
intergrate ϕ*_mϕ_n dτau
what are m and n in the orthonormal equations
they are labels for the different states
orthonormal
If wave functions are orthonormal then m=n and the integral=1, if m does not equal n then the integral will be equal to 0.
