Term

Definition
d^(2)psi 2m[EU(x)]psi(x)
 = 
dx^(2) hbar^(2)



Term

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

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 pontentialenergy 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 lEfEil
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

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(</=) X (</=)
U(x)= infinity X<0 or X>L 


Term

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

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

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

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

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 (n1) nodes and n antinodes (maxima and minima). 


Term

Definition
a quantum particle in a box cannot be at rest
E1 is the zeropoint motion 


Term
Condition for having a Stationary wave 

Definition
the de Brogile waves have to form standing waves 


Term

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


Term

Definition
1. classically forbidden regions are E<U0
2. the wave function on the graph extends into the classically forbidden area
3. there are only a finite number of bound states
4. represent electrons confined to or bound in the potential well
5.no stationary states E>U0 


Term

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

Definition
psi(at x=L)= Be^(L/P.D.)= Psiedge
1. solve for B to get Psi(x)=Psiedge e^((xL)/P.D.) for X (>/=)L 


Term

Definition
P.D. hbar
= 
sqrt(2m(U0E)) 


Term
Quantum Harmonic Oscillator 

Definition
w=sqrt(k/m)
U(x)=.5kx^(2) 


Term
QuantumMechanical 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

Definition
L= sqrt(l(l+1)) hbar l=0,1,2,3..., n1
l is the orbital quantum number 


Term
Zcomponent of the angular momentum 

Definition
Lz= (m)(hbar) m=l, l +1,...,0,..., l1, 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

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

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

Definition
delta l= absolute value of l2l1=1
lamda= (hc)/(deltaEatom) 


Term

Definition
Nexc=N0e^(t/T)
where T=1/r
r is the decay rate =Prob(emission in deltat at time t)/(deltat) 


Term

Definition
Epulse=(Power)(deltat)
Ephoton= hf=(hc)/(lambda)
Epulse=N (Ephoton) 


Term

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

Definition
 r=r0A^(1/3) where r0=1.2fm
 all nuclei have the same density of 2.3 x10^(17) kg/m^(3)



Term

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 shortranged force
 heavier nuclei can become more stable by breaking into smaller pieces
 lighter nuclei can become more stable by fusing together


