Five physics students have a discussion about quantum mechanics, and each one ma

Question

Five physics students have a discussion about quantum mechanics, and each one makes a statement. Only one of them is correct (naturally, she is from UC Davis). Determine which of the following statements are correct or incorrect, and explain why or why not. (a). “There is zero probability for finding a particle in regions where the wavefunction becomes negative, because that would be unphysical.” (b). “If a spin-0 particle decays into two spin-1/2 particles, and Alice measures Sz = +(h-bar)/2 for one of the two particles, then Bob must find that the second particle has Sz = +(h-bar)/2 as well.” (c). “The Hilbert space of a composite particle comprised of a spin-3/2 particle and a spin-7/2 particle is spanned by a total of 32 states.” (d). “ The composite particle formed from this spin-3/2 and spin-7/2 particles has spin 5”. (e). “The expectation value of the momentum of a state |> must vanish in position space because p_x and x do not commute.”

Explanation / Answer

(a). “There is zero probability for finding a particle in regions where the wavefunction becomes negative, because that would be unphysical.”

Ans: False

The wavefunction is either positive or negative that does not mean anything. But the probability amplitude must be positive for physical condition.

(b). “If a spin-0 particle decays into two spin-1/2 particles, and Alice measures Sz = +(h-bar)/2 for one of the two particles, then Bob must find that the second particle has Sz = +(h-bar)/2 as well.”

Ans: False

Here the total spin must be conserved but in the statement the total spin becomes +1 rather than zero. So if Alice measures Sz = +(h-bar)/2 for one of the two particles, then Bob must find that the second particle has Sz = -(h-bar)/2.

(c). “The Hilbert space of a composite particle comprised of a spin-3/2 particle and a spin-7/2 particle is spanned by a total of 32 states.”

Ans: True

Using the spin quantum number which varies from -s to s, the first particle has 4 possible spins (-3/2, -1/2, 1/2, 3/2) and the second particle has 8 possible spins (-7/2, -5/2, -3/2, -1/2, 1/2, 3/2, 5/2, 7/2). then their combination is any of those possibilities (32 states).

(d). “ The composite particle formed from this spin-3/2 and spin-7/2 particles has spin 5”.

Ans: yes if they form in such a way that spin is conserved.

(e). “The expectation value of the momentum of a state |> must vanish in position space because p_x and x do not commute.”

Ans; Yes

The probability of finding momentum certainly in position is space is zero.

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