超星粒子物理期末答案(学习通2023课后作业答案)

1st week: Chapter one

1.1-1 Discovery history of Particle Physics随堂测验

1、超星In photoelectric effect,粒物理期 as for the incident light beam, which restriction for the light is right in the following ?
A、acts more like a wave
B、末答acts more like a particle
C、案学shows the wave-particle duality.
D、习通can be wave and particle both.

2、课后Please examplify at least one case that can justify light is 作业a wave.

3、What is 答案matter wave? who proposed it?

4、Please tell simply the role of the de Broglie wave in pushing forward the building of the quantum mechanics.

1st Exercise

1、超星In Quantum Physics,粒物理期 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?

2、Let's recall what is 末答the quantum in Quantum Mechanics (QM). You may take the angular momentum or other quantum phenomena as examples to understand the concept "Quantum".

3、Please examplify cases as many that the symmetry takes its part.

2nd week: Chapter one

Exercises

1、案学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) ,习通please calculate the coefficient .

2、If the particle obey the following Klein-Gordon equation: .Please prove the current .

3、课后Just as in the exercise 2,作业 the charge is then the integration in the space:, please figure out whether the charge is positive definite or not. Why?

4、Suppose the field is given as in the attachment, please derive the Schrodinger equation from the field given.

5、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): .

3rd week: Chapter one

Exercises

1、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.

2、The Schrodinger equation is known to be , with . Suppose , please derive the equation that is satisfied by .

3、Please prove that the following formula holds for n=2.

4、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.)

5、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 .:

6、For the Klein-Gordon equation please give the proof of its conserved charge:

4th week: Chapter one

3rd Exercises

1、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 .

2、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.

3、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.

4、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 .

5、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.

5th week: Chapter one

Exercises

1、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.

2、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).

6th week: Chapter two

5th Exercise

1、Judge whether following reactions can occur or not. If not, please give the necessary argument against it. (3 points for each).

2、Provided and the Hamiltonian of the classic system is given as , please prove namely the energy is conserved.

3、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)

4、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)

8th week: Chapter three

6th Exercise

1、

2、

3、(10 point for Each)

9th week: Chapter 3 and 4

7th Exercise

1、Please figure out which are formally correct Lagrangians in the following and give your justification simply.

2、(8 points for each)

3、P is parity (spatial reflection) operator, please prove the relation in quantum mechanics.

4、Please use the definition of spherical harmonic function to prove This relation actually gives the eigenvalue of the parity operator.

5、Given a system with the electrons and the electromagnetic interaction between them, please construct the lagrangian for it that includes the electrons and photos and the interaction between them.

10th week: Chapter 4

8th Exercise

1、By setting the intrinsic parity of proton to be , please analyze the system and give the parity of .

2、Similar to above exercise but for As the intrinsic parity of is -1, please give the parity of .

3、, (This problem is subject to the Dirac equations in atomic systems. Correction: The first part gives 15 points. )

4、Use , to figure out the differece of angular momemtum quantum numbers in upper and lower components: (12points). And figure out its impact on the parity of upper and lower components (3 points).

10-11th week: Chapter 4

9th Exercise: violation of parity

1、Please figure out why in the following figure the mirror image cann't exist?

2、For nuclear spin and the momentum of emitted electron please give the proof that (8 points). At the same time, please figure out how to pin down the (5points)

3、Please figure out the relationship between the two-component theory and the helicity of neutrino. What consequence does it have if the neutrino has both the left-handed and right-handed helicities in the weak interaction?

4、Why is the mirror symmetry, left-hand and right-hand symmetry, equivalent to the space reflection (parity)?

11-12th week: Chapter 5

10th Exercise

1、Please figure out whether the 5 processes in the figure denoted by the yellow double arrows can take place, and justify your answers briefly:

2、Please figure out briefly what is the real CP symmetry violation in neutral kaon decay.

3、In the K0 decay, K1 and K2 were domenstrated to be an equal mixing of . Inversely, can be re-expressed by K1 and K2. Assume that the amplitudes of |K1> and |K2> are please prove the probability of varies with time as

4、Why can the CP symmetry breaking tell that the quarks should have 3 generations?

13th week: Chapter 6

11th Exercise

1、证明：

2、

3、Please prove the proton and antiproton have the same mass according to the CPT theorem.

14th Week Chapter 7

12th Exercise

1、For the global SU(2) symmetry, one transforms the nucleons in isospin space with the known generator In isospin space the proton can be written as please evaluate and see what will amaze you by such a transformation which is actually the rotation in isospin space.

2、Please make a table to give the hypercharge (Y), 3rd component of isospin , and strangeness (S) for following particles: and check whether the Gellmann-Nashijima relation holds.

Exercise for mutual grading

1、The Lagrangian for the system is given by To keep it invariant under the local gauge transformation Please prove the transformation of gauge field satisfies the following formula:

15th Week Chapter 7: Spontaneous symmetry breaking

13th Exercises

1、Please prove the relation:

2、Knowing please prove the lowest-energy state (2) by redefining the field upon the vacuum

Chapter 8: Standard model and quark structures

14th exercises

1、Please figure out main sectors of the standard model as possible as you can.

2、Please write out the elementary particles in the Standard Model, and figure out its total number.

3、The Gellmann-Okubo mass formula for baryons is given as please determine the coefficients using the baryon masses for nucleons (938 MeV), and hyperons whose isospins are respectively. (10 points). Then please evaluate the mass of using above mass formula and compare it with that in the courseware. (4 points)

4、Make sure you know the charge of (u,c,t:2/3) (d,s, b:-1/3) quarks. Please write all possible quark flavors for following baryons and count the their charges:

5、Please exemplify at least 3 hadrons featuring strangeness, and 3 hadrons featuring charm quark constituents.

6、

学习通粒子物理

粒子物理是研究物质的最基本组成部分和它们之间的相互作用的科学。它涉及到极小的“粒子”，如原子核和元素粒子，以及它们之间的相互作用和转化。粒子物理是一门极其复杂和困难的学科，它需要掌握深厚的理论知识和高超的实验技术。而学习通作为国内知名的职业教育平台，为广大学习者提供了粒子物理学习的机会。