2021 粒子物理(东南大学) 最新满分章节测试答案

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本课程起止时间为:2021-03-02到2021-07-11
本篇答案更新状态:已完结

【作业】1st week： Chapter one 1st Exercise

1、 问题: In Quantum Physics, we learnt the microscopic particles obey the Schrodinger equation whose solution is the wave function. The question thus arises naturally: What is the Particle in Particle Physics?
评分规则: 【 It’s a Quantum. Wave and particle duality.
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2、 问题: Let’s recall what is the quantum in Quantum Mechanics (QM). You may take the angular momentum or other quantum phenomena as examples to understand the concept “Quantum”.
评分规则: 【 Quantized numbers like energy quantum in photoelectric effect and angular momentum l which is an integer in unit of h bar.
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3、 问题:Please examplify cases as many that the symmetry takes its part.
评分规则: 【 The Calendar, the Sun, the Moon, the Clock, Conserved angular momentum of rotational symmetry; Conserved energy in time of temporal symmetry; Conserved momentum (velocity) in space with spatial symmetry…….
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【作业】2nd week： Chapter one Exercises

1、 问题:Assume that a and are in turn annihilation and creation operators subject to the harmonic oscillator potential. (1) Please give explicitly the x and p in terms of these operators. (2) ,please calculate the coefficient .
评分规则: 【 x,
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2、 问题:If the particle obey the following Klein-Gordon equation: .Please prove the current .
评分规则: 【 Write down the conjugate equation for , then make the difference
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3、 问题:Just as in the exercise 2, the charge is then the integration in the space:, please figure out whether the charge is positive definite or not. Why?
评分规则: 【 Not, because of the derivative.
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4、 问题:Suppose the field is given as in the attachment, please derive the Schrodinger equation from the field given.
评分规则: 【 Just Schodinger equation.
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5、 问题:The commutator plays a fundamental role in Quantum Mechanics (QM). So does in Quantum Field Theory (QFT). Since the wave functions in QFT, represented by the operators , are also operators, please figure out the simultaneous commutator for the fields (in the harmonic oscillator motion): .
评分规则: 【
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【作业】3rd week： Chapter one Exercises

1、 问题:Let be the annihilation and creation operators of the fermion, respecitively. Thus, it has the relations: is the particle number operator. Please prove N just has eigen value 1 or 0.
评分规则: 【
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2、 问题:The Schrodinger equation is known to be , with . Suppose , please derive the equation that is satisfied by .
评分规则: 【
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3、 问题:Please prove that the following formula holds for n=2.
评分规则: 【
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4、 问题:Let the operator be , please prove the vacuum expectation value of (normal product) is zero, namely . Note this represents a kind of the interaction between fermions and boson with g being the coupling constant. (hint: the fields can be expanded by plane waves.)
评分规则: 【 According to the definition of normal product of operators.
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5、 问题:The Dirac eqation describes the motion of fermions. As you watched the video to derive the Dirac equation, you would find that the wave function consists of and : . Later on, we will understand that this is actually a spinor with different rotational motions for R and L components. Please start from a travelling wave for to obtain the following Dirac equation. Also please derive explicitly the matrices .:
评分规则: 【 Watch the video carefully and follow the detail to obtain the equation.
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6、 问题:For the Klein-Gordon equation please give the proof of its conserved charge:
评分规则: 【 From the difference between the Klein-Gordon equation and its complex conjugate form, we can get the conserved current and the fourth component, the charge.
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【作业】4th week： Chapter one 3rd Exercises

1、 问题:Suppose a particle from the initial state scatters off a massive target to a final state . The target is at x=0, and the field of the particle is given aswith being the annihilation operator. The scattering occurs at x=0 means that an annihilation operation of is succeeded by a creation operation of at x=0. Please justify the relation .
评分规则: 【 , for nonzero transition probability in the integration in a wavelength, the exponent shoud be 1 which means the relation should be tenable.
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2、 问题:Similar to Exercise 1, but now consider two-particle scattering. The internal line is expressed by , the transition matrix element is written as . please give the proof for the momentum and energy conservations at vertices. As shown in the figure, the momenta and positions are marked.
评分规则: 【 Write down explicitly the integration in the transition matrix element. You will find two exponential factors: . To have nozero result, the 4-momentum conservation is naturally required.
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3、 问题:Suppose the typical cross section is 200 mb for strong interaction reactions, like in the reaction . Please estimate the order of magnitude of the cross section of the reaction: which is dictated by the weak interaction. The incoming and outgoing energies are assumed to be same as those in the strong interaction case.
评分规则: 【
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4、 问题:For the static potential for electric field, it is This is actually related to the photon propagator ,with while for static case, . Please prove the relation .
评分规则: 【 First calculate ,(8 points)Then use relation: (8 points)
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5、 问题:Similar to Exercise 1, but with massive mesons. The static meson propagator can be written as , Please prove: the corresponding potential V is given as ,(hint: the meson’s equation of motion is given as , then take the static case). Note that there would be a minus sign for V(r), but it doesn’t matter.
评分规则: 【 two steps similar to Exercise 1
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【作业】5th week： Chapter one Exercises

1、 问题:About the natural unit. Given that and at the energy scale MeV, which shows that a 1 fm body is roughly of that energy. Please calculate at energy scales: eV and , with the latter being the Planck energy scale.
评分规则: 【 I wait for your answers. 1st is of 6 points, second 8 points.
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2、 问题:Suppose the free neutron gas with the Fermi momentum , (1) please calculate the neutron Fermi energy, given its mass is 938 MeV (6 points). (2) please figure out how many neutrons in a volume of , as its degeneracy is 2 (spin up and down). (10 points).
评分规则: 【 1) 2) ,
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【作业】6th week： Chapter two 5th Exercise

1、 问题:Judge whether following reactions can occur or not. If not, please give the necessary argument against it. (3 points for each).
评分规则: 【 1）Yes. 2)Yes. 3) No, violation of energy conservation. 4) No, violation of baryon number conservation. 5) No, violation of charge conservation. 6)No, violation of lepton number conservation. 7) Yes.
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2、 问题:Provided and the Hamiltonian of the classic system is given as , please prove namely the energy is conserved.
评分规则: 【 Let us write the explicit temperol derivative of the Hamiltonian:(5 points) and (4 points). Now, it has, by using the Euler-Lagrange equation . (5 points).
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3、 问题:In quantum systems, the temporal translation , leads to the transformation of wave function: . please prove the energy conservation under infinitesimal temporal and finite temporal transformations. (10 points for each)
评分规则: 【 Starting from the expansion for infinitesimal :…….
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4、 问题:Provided that there is the invariance under the rotation about the z-axis. Please prove that this invariance gives rise to the conservation of in either classic case or the infinitesimal rotation for the quantum case (do one in two cases ). (10 points)
评分规则: 【 I just wait for your answers.
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5、 问题:please prove the above Maxwell equations are invariant under Lorentz transformation.