Quantum Physics

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Consider a particle whose wavefunction at some fixed time t is represented by
-A if -2≤x≤0
ψ(x)= A if 0≤x≤3
0 otherwise
(a) What is the normalization constant A?

(b) What is the probability of finding the particle at a position x≤0?

(c) What is the expected value of position x?

(d) What is the expected value of momentum p?

• Quantum Physics -

|psi(x)|^2 integrated from minus to plus infinity is 5 |A|^2, this has to be equal to 1, therefore you can choose A as 1/sqrt(5) (you are free to multiply this by any phase factor
exp(i theta)).
The probability of the aprticle being at negative x is the integral from minus infinity to zero of |psi(x)|^2 dx, which is 2/5.

Expacted position: Integrate

x |psi(x)|^2 dx from minus to plus infinity, you get <x> = 1/2.

• Quantum Physics -

And, of course <p> = 0, because the fact that psi(x) is (or can be chosen to be a) real function of x, implies that the modulus squared of the momentum space wavefunction
psi(p) is an even function of p. To see this, note that:

psi(x) = 1/sqrt(2 pi hbar) Integral from minus to plus infinity of
dp psi(p) exp(i p x/hbar)

Take the complex conjugate of this:

psi*(x) = 1/sqrt(2 pi hbar) Integral from minus to plus infinity of
dp psi*(p) exp(-i p x/hbar) =

1/sqrt(2 pi hbar) Integral from minus to plus infinity of
dp psi*(-p) exp(i p x/hbar)

Since psi*(x) = psi(x), this means that

psi*(-p) = psi(p)

therefore

|psi(-p)|^2 = psi*(-p)psi(-p) =

psi(p)psi*(p) = |psi(p)|^2

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Answers to q6 and 8 ?

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prob 3 C

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3C is 3/2
6A is pi/2 and pi/4
6B is 1/2 and 1/2
Looking for 6C and 6D
8A is 1/2, 1/2, 0, 0
8B is 0, 0, 1/2, 1/2
8C is 1, 1, 0, 0
Looking for 8D and 8E
8F is No

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Thank you.
And waiting for the rest answers

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5 plz....

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7a 1/2 7b 1/2

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Problem 9 plzz

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8D ,8E,6C,6D and 9

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9 is 175.8

Anyone 8D ,8E,6C,6D?

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4a,b,c,d plz ?

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for 4 some one already gave you so you have:

4a: 1/sqrt(5)
4b 2/5
4c 1/2
4d 0

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thx very much helper

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5 plz?

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5A i 0 0 -i 5b -i 0 0 i 5C -1 -1 -1
3a is 2nd option 3b is 2nd option

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8c = 1, 1, 0, 0
8D= 1/n,1/n,0,0,1/n,1/n,

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JLG - Thanks for 8D and 8E. Didn't realize n was acceptable.
Anyone have 6C and 6D?
5 a) {{i,0}{0,-i}}
5 b) {-{i,0}{0,i}}
5 c) -1, -1, -1

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6C and 6D

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6c: 1/2+1/(2*sqrt(2)
1/2-1/(2*sqrt(2)
6D I continius lost..

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6D is the same that 6 C :)

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8e: 0,1/n, 1/n

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Thanks JLG

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THANKS

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THANKS ANNE

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6c second part ans. is not accepted,,,wat is its numerical value.

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Hey Guys... Ready for the final??

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Helloo Any answer for the Final?

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1] Given qubit 1 in the state 35|0>+45|1> and qubit 2 in the state 12√|0>+i2√|1>, what is the state of the composite system?
in form of a│00> + b│01> + c│10> + d│11>
find a b c d.

2] Which of the following states is entangled?
a) |++>
b) 45|01>−35|11>]
c) 1/√3|01> +1/√3|10>−1/3|11>
d) 1+i/√22|++> − 1+i/√22|+−>
+ 1−i/√22|−+> − 1−i/√22|−−>