How do we define kinetic enery of a particle in quantum
What is root purpose of schreodinger
Ties the waveform, momentum and energy of a particle together so that we can relate all three to each other.
Given the potnetial energy, the deffinite energy; we can solve ofor wavefunction.
What is the form of hte time independent shreodinter euqation
It is used most commonly when we wish to relatede potential energy, actual energy and
What is the condition for orthognality of two vectors
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What is the condition for normalizing a vector
To normallize, if not equal to 1, sqrt(1/ans) = N
Hamiltonian operator interms of time and planck
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Linier Momentum Operatort px
Hamiltonian operator in 3d momentum
Energy in terms of momentum
Postulate 1 of quantum: the state vector rule
The state of a quantom at a tiven moment can be described using a normalized state vector having as many complex components as there are possible values for objects observable qualities.
|\ |^{2}Is the chance of finding a particle in the box formed by xyz +dxdydz at time t
Postulate 2 :
For every observable propoerty there is a linier hermitian operator that connects wave to classical behavior
Postulate 3: How to find psi
i
Solving time dependent shredigner will allow wavefunction to be found
LInier operator condition
an object is a linier operator if
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Commutation
If the order of operations is irrelevent, then two operators commute, and if two operators commute on an eigenfunction, then then any eigenfunction of one is also an eigenfunction of the other.
Kinetic Energy Operator
Calculating binding energy of molecular solids
Molecular solids are london and van der waal based
function of
Calculating binding energy of hydrogen bond solids
These are items witha strong difference in electronegativity between components. They have part positive part negative
Crystal bond is function of Leonard Jones
Modelled with partial dipole charges
Metallic crystal bonding data
Calculated with density functional theory 15% accurate for first 50 elements
Sea of electrons hold together
Energy = enthalpy of sublimation
Covalent Crystals
Share electrons
Energy calculated as function of density functional theory
Roughly equal to sublimation enthalpy
Ionic molecule
Intra molecular bond of ionic crystals
Function of bond charges and radius
What type of bond in SiO_{2 }Quartz
Covalent
What kind of solid is nitrogen
Covalent
Latice enthalpy of a ionic crystal
heat sublimation (solid) + Heat vap (gas) +.5 Dissociation (gas) + ionization energy (solid)-electronaffinity (gas)-Heat of formation (crystal)
Langmuir hinschelwood surface
Requires a and b to bond next to each other on surface
A and b then react
Peak and then decline
How do we account for effect of temperature on adsorption?
Van't hoff equation...
Finding hads
PLot : ln (P) vs 1/T
Slope = incH/R
What happens to adsorption when temp rise
Adsorption decline per le chatleir principle
Langmuir Rideal
A and b bond competitively to surface
A needs to be in gas Phase and B bonded to surface for reaction.
Speed of Light vs wave qualities
c= wavelength*frequency
Energy in quantum mech relation to planc
Blackbody failure
Classic physics (rahleigh jean)assumed would increase as v/t increase
QUantum showed peak followed by decline as function of probabillity of different energy levels (Planck, wein)
Photoelectric failure
Classic physics predict that energy of ejected electrons depend on light
In quantum, shown that in fact energy of ejected electrong depend on frequency (hv)
Work function
hv= Kinetic Energy+w
Photon dual theory
Photons have both wave and particle effects
Difraction and interference are functions of wave
PHotoelectric is function of particle
Bohr stationary state
Stated that elecrong has stome sttionary state in which it does not emit EM radiation
Boher energy to move between states
hv= E_{2}-E_{1}
Shows spectral frequency of an electron moving between energy states
Relation between momentum and velocity
p=mvel
Psi must be well be haved. What does well behaved mean (33 criterea)
Singel valued
Smooth and continuous (function and derivative)
Postulate 4: Measurement to eigenvalue connection
States that for an operator F, ther corespanding eigenvalues f crepresent all possible values of that physical quantity
Deffining aeigenvalue
If A_hat is an operator and a is a constant and g is some function
So long as then g is an eigenfunction
Postulate 5: expected values
if we have some value f we wish to find, teh average value will be
\bar F =
Zero POint energy of a particle
Lowest possible energy (can be less than zero)
Nodes related to quantum enegy
Nodes = n-1
Energy in quantum, vs classic
Quantum does not allow all energy levels, classic does
Comparison of quantoum to classic enegy lowest
Lowest energy is not zero in quantum, it is in classic
Location of particle in quantum vs classic
In quantum there ar non equal possible locations and forbiden zones, in classical, all are equally possible.