# Shared Flashcard Set

## Details

Modern Midterm 2
N/A
51
Physics
11/14/2012

Term
 Schrodinger Equation
Definition
 d^(2)psi      -2m[E-U(x)]psi(x)                      ---------- =    ---------------------                                     dx^(2)              hbar^(2)
Term
 de Brogile Wavelength
Definition
 it increases as the particle's kinetic energy decreases
Term
 When is the de Brogile wavelength the same at all positions?
Definition
 if U is constant then K is constant, thus the de Brogile wavelength is the same at all positions
Term
 What is the relationship between the de Brogile wavelength with K
Definition
 inverse relationship...as K increases the wavelength decreases
Term
 When can you solve the Schrodinger equation?
Definition
 It can't be solved until U(x) has been specified
Term
 Boundary Conditions
Definition
 The conditions or restrictions on acceptable solutions
Term
 Primary Conditions a Wave Function must obey:
Definition
 1. psi(x) is a continuous function 2. psi(x)=0 if x is in a region where it is physically impossible for the particle to be. 3. psi(x) --> 0 as x--> +infinity and x --> -infinity 4. psi(x) is a normalized function
Term
 General Solution for psi(x)
Definition
 psi(x)= Apis1(x) + Bpsi2(x)
Term
 How to solve a quantum mechanics problem
Definition
 1. Determine a pontential-energy function. 2. draw the potential energy curve 3. establish the boundary conditions that the wave function must satisfy. 4. normalize the wave functions 5.draw graphs of psi(x) and lpsi(x)l^(2) 6. determine the allowed energy levels 7. calculate probablities, wavelengths, or other quantities
Term
 What are the solutions to the Schrodinger equation?
Definition
 The stationary states of the system
Term
 Jumping from one stationary state to another
Definition
 deltaE     lEf-Eil                           f = ------- =  --------                                   h            h
Term
 What does a standing de Brogile wave lead to?
Definition
 It leads to an energy quantization; only discrete energies allowed
Term
 Rigid Box
Definition
 a box whose walls are so strudy that they can confine a particle no matter how fast the particle moves.
Term
 Characteristics of a Rigid Box
Definition
 1. The can move freely between X=0 and X=L at a constant speed; constant K. 2. No matter how much K, the turning points are at 0 and L. 3. The regions x<0 and x>L are forbidden. The particle cannot leave the box.
Term
 Potential Energy for a Rigid Box
Definition
 U(x)= 0            0(L
Term
 Finding the Wavefunction
Definition
 1. since U(x)=0 then the second derivative of psi in respect to x is   -2mEpis(x)                                          =  ------------                                               hbar^(2) 2. Beta^(2)   2mE                 = ------                     hbar^(2)
Term
 What functions second derivative is a negative constant times the function itself?
Definition
 psi1(x)=sin(Betax)          psi2(x)=cos(Betax) 2. Then you take the second derivative of each psi and put it in the psi(x)=Apsi1(x) + Bpsi2(x)
Term
 Why B=0?
Definition
 For x=o psi(x)=o for this condition and the B part does not fit the property.
Term
 Where X=L: psi(x=L)=Asin(betaL)=0
Definition
 1. solve for (beta)*(L); so find a constant that helps achieve sin(betaL)=0 2. solve for beta and plug it into psi(x)
Term
 Solving for Energy
Definition
 since Beta     sqrt(2mEn)    npi                =   ---------  =  -----       n=1,2,3...                       hbar           L 2. solve for energy En=n^(2) h^(2)/8mL^(2)=n^(2)E1.
Term
 Energy En
Definition
 1.these are the only values forE for which there are physically meanigful solutions to the Sch. equation. 2. it is the energy of the stationary state with quantum number n 3. E1 is the ground state energy
Term
 Normalizing the equation
Definition
 1. equation on reference sheet. 2. solve for An, which seems to always equal sqrt(2/L).
Term
 Nodes and antinodes for psi(x)
Definition
 has (n-1) nodes and n antinodes (maxima and minima).
Term
 Zero-Point Motion
Definition
 a quantum particle in a box cannot be at rest E1 is the zero-point motion
Term
 Condition for having a Stationary wave
Definition
 the de Brogile waves have to form standing waves
Term
 Correspondence Principle
Definition
 Bohr's idea that the quantum world should blend smoothly into the the classical world for high quantum numbers.
Term
 What is the probability of finding a classical particle within a small interval dx
Definition
 the fraction of its time that it spends passing through dx Probclass(in dx at x)=(dt/.5T)= (2/Tv(x))
Term
 Classical Probability density
Definition
 Pclass(x)=1/L
Term
 Finite Potential Wells
Definition
 1. classically forbidden regions are EU0
Term
 Finite Potential 2
Definition
 1. because the wave functions are slightly more spread out, you get a lower velocity and thus lower energy.
Term
 Classically Forbidden Region
Definition
 1. e^(x/P.D.) and e^(-x/P.D.) are used where psi(x)=Ae^(x/P.D.) + Be^(-x/P.D.)   for x greater than or equal to L 2. psi-->0 as x-->infinity 3. since e^(x/P.D.) diverges as x--->infinity A=0
Term
 Psi edge
Definition
 psi(at x=L)= Be^(-L/P.D.)= Psiedge 1. solve for B to get Psi(x)=Psiedge e^-((x-L)/P.D.) for X (>/=)L
Term
 Pentration Distance
Definition
 P.D.          hbar       =  ---------------             sqrt(2m(U0-E))
Term
 Quantum Harmonic Oscillator
Definition
 w=sqrt(k/m) U(x)=.5kx^(2)
Term
 Quantum-Mechanical Tunneling
Definition
 1. A higher total energy line means a larger K not a higer elevation 2. tunnels its way through the hill and emerges on the other side 3. requires not expenditure of energy
Term
 Energy for Hydrogen ch.42
Definition
 En= -13.60eV/n^(2)  n=1,2,3 n is the principal quantum number
Term
 Angular Momentum
Definition
 L= sqrt(l(l+1)) hbar  l=0,1,2,3..., n-1 l is the orbital quantum number
Term
 Z-component of the angular momentum
Definition
 Lz= (m)(hbar)   m=-l, -l +1,...,0,..., l-1, l m is the magnetic quantum number
Term
 Angular Momentum is Quantized
Definition
 thetalm=cos^(-1)(Lz/L)  ground state of l=0 has no angular momentum
Term
 Ionization Energy
Definition
 absolute value of E1=13.60eV, is the minimum energy that would be needed to form a hydrogen ion by removing the electron from the ground state.
Term
 Otto Stern and Walter Gerlach
Definition
 1. prepare an atomiv beam by evaporating atoms out of a hole in an oven 2. an atom whose magnetic moment vector mnu is tilted upward (mnu >0) has an upward force on it's north pole that is larger than the downward force on its south pole. 3. a downward tilted magnetic moment (mnu<0)experiences a net downward force  4. A magenetic moment perpendicular to the field (mnu=0) feels no net force and passes through the magenet with no deflection.
Term
 Spin Quantity Number
Definition
 1. ms= (+/-)1/2 2. spin up state is the positive and spin down is the negative 3. The electron's spin is an intrinsic quantum property of the electron that has no classical counterpart
Term
 Excitation :Absorption
Definition
 delta l= absolute value of l2-l1=1 lamda= (hc)/(deltaEatom)
Term
 The Decay Equation
Definition
 Nexc=N0e^(-t/T) where T=1/r r is the decay rate =Prob(emission in deltat at time t)/(deltat)
Term
 Laser
Definition
 Epulse=(Power)(deltat) Ephoton= hf=(hc)/(lambda) Epulse=N (Ephoton)
Term
 Isotopes
Definition
 the atoms of an element with different values of A; where A=Z+N only 266 are stable isobars- same A but different Z and N
Term
 Nuclear Size and Density
Definition
 r=r0A^(1/3) where r0=1.2fm all nuclei have the same density of 2.3 x10^(17) kg/m^(3)
Term
 Binding Energy
Definition
 The energy you would need to supply to a nucleus to disassemble it into individual protons and neutrons B=(ZmH +Nmn - matom) x(931.49) peaks ingraph are due to closed shells nuclear force is a short-ranged force heavier nuclei can become more stable by breaking into smaller pieces lighter nuclei can become more stable by fusing together
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