Exercise 8.15 Consider a system of two noninteracting identical spin 1/2 particles (with mass m) that are confined to move in a common one-dimensional harmonic oscillator potential. Assume that the particles are in a state with the wave function Y(x1, x2) = √2 π.χ. ² (-1/23 __x² + x² 2x3 (x2-x1) exp X (S1, S2), where x₁ and x2 are the positions of particles 1 and 2, respectively, and x (s1, s2) is the spin state of the two particles. (a) Is x (S1, S2) going to be a singlet or triplet state? (b) Find the energy of this system.
Exercise 8.15 Consider a system of two noninteracting identical spin 1/2 particles (with mass m) that are confined to move in a common one-dimensional harmonic oscillator potential. Assume that the particles are in a state with the wave function Y(x1, x2) = √2 π.χ. ² (-1/23 __x² + x² 2x3 (x2-x1) exp X (S1, S2), where x₁ and x2 are the positions of particles 1 and 2, respectively, and x (s1, s2) is the spin state of the two particles. (a) Is x (S1, S2) going to be a singlet or triplet state? (b) Find the energy of this system.
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Transcribed Image Text:Exercise 8.15
Consider a system of two noninteracting identical spin 1/2 particles (with mass m) that are
confined to move in a common one-dimensional harmonic oscillator potential. Assume that the
particles are in a state with the wave function
Y(x1, x2) =
√2
√ XO
(x2-x1) exp
_x³ + x²
x
X (S1, S2),
where x₁ and x2 are the positions of particles 1 and 2, respectively, and x ($1, s2) is the spin
state of the two particles.
(a) Is x ($₁, $2) going to be a singlet or triplet state?
(b) Find the energy of this system.
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