Quantum (Haehner) Flashcards
equation for frequency?
v = dE/h
what energies can v possess (looking at particle character of EM radiation)
0, hv, 2hv…
what is p in the de broglie equation?
linear momentum
what is the de broglie equation?
[lambda] = h/p
how do diffraction patters arise?
from many waves interfering constructively and destructively
what is h bar?
h/2pi - planck’s constant which takes angular momentum into consideration
general schrodinger equation?
HY=EY
what is the schrodinger equation for a particle in a 1D box?
-(hbar^2/2m)*(d^2[psi]/dx^2) + V(x)[psi] = E[psi]
give some examples of observables
momentum, energy, position
what is the position operator?
x[bar]=x*…
what is the momentum operator?
p[bar]x = h(bar)/i*d/dx…
What is the Born interpretation?
gives the probability of finding a particle between x and xdx
what is the equation for probability density?
|[psi]x|^2
what is the expectation value?
the average value of a large number of observations
3 steps to forming a schrodinger equation?
1) write down the total energy in terms of kinetic and potential
2) replace momentum and position in the energy equation with appropriate operators
3) then solve the SE to obtain eigenstates and eigenvalues.
What is a polar coordinate?
A 2D system of coordinates where all points are referenced off a central point by distance and angle
What symmetry does potential energy in the schrodinger equation have?
centrosymmetric
What can polar coordinates do to the schrodinger equation?
split it into radial and angular components
What are spherical harmonics?
the normalised wave functions of the angle dependent part of the schrodinger equation.
What is a hydrogen atom?
an atom or ion with only 1 electron
What is the equation for the Coulomb interaction of an electron with a nucleus?
V(r) = - Ze^2 / 4[pi][eo]r
What is the equation for the eigenvalues for the hydrogen atom?
En = -Z^2[mu]e^4 / 32[pi]^2[eo]^2h(bar)^2n^2
What is a boundary surface?
the area in which you are most likely to find an electron in an orbital - the shape of the orbital
What is the Born-Oppenheimer approximation?
oscillations from e- arrangement to equilibrium position moves faster than nuclei –> so the wavefunction can be separated into smaller components