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Flashcards in Chp1 Deck (24)
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1
Q

P(particle in [a,b])

A

integral a-b of mod(phi(x))^2

2
Q

DEfn: normalised

A

integral mod(phi(x))^2 =1

3
Q

Defn: position Operator: x~=

A

x

4
Q

Defn: Momentum Operator: p~

A

-ih(d/dx) (partial)

5
Q

Defn: Energy Operator: H=

A

p~^2/2m + V(x~)=-h^2(d^2/dx^2)phi+V(x)phi(x)

6
Q

DEfn: Time-dep SE:

A

ih(dPHI/dt)=H(PHI)

ih(dPHI/dt)=-(h^2/2m)(d^2/dx^2)PHI +V(x)PHI

7
Q

Defn: Stationary state: Phi(x,t)=

A

phi(x)exp(-iEt/h)

phi(x) is an efn of H with eval E

8
Q

Conservation eqn for P(x,t):

A

dP/dt=-dj/dx

9
Q

j(x,t)=

A

-ih/2m(PHIdPHI/dx-dPHI/dx*PHI)

10
Q

Defn: Inner Product

phi,theta

A

integral phi(x)*theta(x)dx

11
Q

Defn: Norm of phi

A

(phi,phi)=integral mod(phi)^2 dx

12
Q

Defn: phi=

A

(phi,Hphi)

13
Q

Defn: Uncertainty

(Dx)^2=

A

)^2>=-^2

14
Q

Defn: Q is Hermitian iff

A

(phi,Qtheta)=(Qphi,theta)

(Q real) x~,p~ and H all fit

15
Q

Prop: Cauchy-Schwarz

A

norm(phi)norm(theta)>=mod((phi,theta))

16
Q

Thm: Ehrenfest’s

A

d/dt=1/m<p>

d/dt</p><p>=-</p>

17
Q

Thm: Heisenberg uncertainty

A

(Dx)(Dp)>=h/2

18
Q

Defn: Commutator: [Q,S]=

A

QS-SQ

19
Q

[x~,p~]

A

ih

20
Q

Defn: Wavepacket

A

A wavefn localised in space

21
Q

Defn: Gaussian Wavepacket

A

PHI(x,t)=(a/pi)^(1/4)1/sqrt(g(t)) e^(-x^2/2g(t))

22
Q

correct g(t) for G wavep to solve tdep SE

A

a+ih/m t

23
Q

Thm: General Ehrenfest

A

ihd/dt= {+ih}

24
Q

Defn: Degeneracy

A

The dimension of the espace of eval l