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

  • Quantum Physics -

    Answers to q6 and 8 ?

  • Quantum Physics -

    Please q6 and q8 !

  • Quantum Physics -

    prob 3 C

  • Quantum Physics -

    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

  • Quantum Physics -

    Thank you.
    And waiting for the rest answers

  • Quantum Physics -

    5 plz....

  • Quantum Physics -

    7a 1/2 7b 1/2

  • Quantum Physics -

    Problem 9 plzz

  • Quantum Physics -

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

  • Quantum Physics -

    9 is 175.8


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

  • Quantum Physics -

    6C,6D,8C,8D please..

  • Quantum Physics -

    4a,b,c,d plz ?

  • Quantum Physics -

    for 4 some one already gave you so you have:

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

  • Quantum Physics -

    3a and b please

  • Quantum Physics -

    thx very much helper

  • Quantum Physics -

    5 plz?

  • Quantum Physics -

    5A i 0 0 -i 5b -i 0 0 i 5C -1 -1 -1
    3a is 2nd option 3b is 2nd option
    6C,6D,8C,8D please

  • Quantum Physics -

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

    Please 6C and 6D

  • Quantum Physics -

    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

  • Quantum Physics -

    6C and 6D

  • Quantum Physics -

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

  • Quantum Physics -

    6D is the same that 6 C :)

  • Quantum Physics -

    thx all, 8e please

  • Quantum Physics -

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

  • Quantum Physics -

    Thanks JLG

  • Quantum Physics -

    THANKS

  • Quantum Physics -

    THANKS ANNE

  • Quantum Physics -

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

  • Quantum Physics -

    Hey Guys... Ready for the final??

  • Quantum Physics -

    Helloo Any answer for the Final?

  • Quantum Physics -

    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|−−>

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