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ฟิสิกส์โอลิมปิก วิทยาศาสตร์โอลิมปิก ข้อสอบแข่งขัน ข้อสอบชิงทุน => GRE - Physics => Topic started by: conantee on January 08, 2010, 01:54:18 AM

Title: GR8677.089
Post by: conantee on January 08, 2010, 01:54:18 AM
89. A system containing two identical particles is described by a wave function of the form
\psi = \frac{1}{\sqrt{2}} [\psi_\alpha (x_1) \psi_\beta (x_2) + \psi_\beta (x_1) \psi_\alpha (x_2)]
where x_1 and x_2 represent the spatial coordinates of the particles and \alpha and \beta represent all the quantum numbers, including spin, of the states that they occupy. The particles might be
(A) electrons
(B) positrons
(C) protons
(D) neutrons
(E) deuterons

Title: Re: GR8677.089
Post by: conantee on October 15, 2010, 11:39:16 AM
The key here is plus sign in the middle of wave function. It means that both particles can occupy a same state. This kind of particles is called bosons (integral spin).

(A) is clearly wrong. You have Pauli exclusion principle for electron. Electron is not boson.
(D) is also wrong. Neutron star is a kind of example. Since they cannot occupy a same state, they pile up as a star.
(B) is wrong since positron is just the antiparticle of electron. It still carries 1/2 spin. (Pair production is a good evidence, electron has 1/2 spin, so positron does to conserve angular momentum).
(C) is wrong. Basically, protons are pretty much same as neutrons, except slight mass and charge.
(E) is the correct answer. Its spin is 1/2 +1/2, from neutron and proton. Hence, it has integral-spin property.

The correct answer is (E). 31 of 100 people answer correctly.

Note: conclusion: electron, proton, neutron, and their antiparticles are fermion (half spin) , while photons, other force carriers, and pair of fermions are bosons (integral spin).