For the deuteron, L = 0,2 S=1 and J=1. The total wavefunction must be antisymmetric. a)...
For the deuteron, L = 0,2 S=1 and J=1. The total wavefunction must be antisymmetric.
a) Explain why the spatial part must be symmetric.
b) Show why the spin part must also be symmetric.
c) For the antisymmetric system, what is the only allowed value of T and the corresponding isospin wavefunction?
Homework Answers
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For the deuteron, L = 0,2 S=1 and J=1. The total wavefunction
must be antisymmetric.
a)...
Question 1 (8 marks in total) The deuteron is a bound state of a proton and a neutron. Treating nucleons as identical particles with spin and isospin degrees of freedom, the total state of the deuter...
Question 1 (8 marks in total) The deuteron is a bound state of a proton and a neutron. Treating nucleons as identical particles with spin and isospin degrees of freedom, the total state of the deuteron can be writ- ten space Ψ spin Ψ isospin. The deuteron has a total angular momentum quantum number J - 1 and a total spin S -1. Our goal is to determine the parity of the deuteron Q1-1 (1 mark) Show that the possible...
Problem 4 Imagine that a pion π-is captured by a deuteron nucleus fron a p-orbit with...
Problem 4 Imagine that a pion π-is captured by a deuteron nucleus fron a p-orbit with spin 1 eventually converted to two neutrons through strong interaction. (a) What are the possible values of the orbital angular momentum for the neutron pair? (b) Show that the neutron should be in a spin singlet state. (c) Repeat part (a) and (b) if the deuteron is in s-state with spin 1. Hint: The parity of the deutcron is +1. Assumc that the pion...
1. (a) (10 pt) Which of the following wavefunctions CAN be a valid total wavefunction for...
1. (a) (10 pt) Which of the following wavefunctions CAN be a valid total wavefunction for the excited electronic state of He: 2p13d1 with the total electron spin in the triplet state (25+1 = 3), where N is the normalization constant. Explain your choice. (i) NW2p(1)3d(2) [0(1)(2)-6(1)a(2)] (ii) N [42p(1)93a(2) - za142p(2)] [a(1)B(2)+B(1)a(2)] (iii) N (42p(1)43a(2) + Y3d(1)420(2)) [a(1)$(2)-B(1)a(2)] (iv) N (42p(1)^3a(2) - 43a(1)#2p(2)] a(1)a(2) (b) (10 pt) Determine the normalization constant N in the following wavefunctigo: N [Uzo(1)3d(2) W3d(1)42p(2))...
Tl 6. (4 pts) We calculated Ahf for the ground state Hydrogen atom, but now let us consider Hht f...
Tl 6. (4 pts) We calculated Ahf for the ground state Hydrogen atom, but now let us consider Hht for the ground state of the deuterium atom. The basic idea is the same: Here the matrix representation of S is the same, since it represents the spin operator for the spin- electron, but that of 7 is different because the deuteron is a spin-1 particle (neutron+proton) whose spin has 3 possible values for the magnetic quantum number. Also, we must...
3. Knowing that the magnesium and aluminum atoms possesses 12 and 13 electrons respectively: (a) Write...
3. Knowing that the magnesium and aluminum atoms possesses 12 and 13 electrons respectively: (a) Write down the electron configuration (nl) of the ground state. Explain your answer. (b) We focus on the electron configuration determined in (a). Considering only the electrons from the outer subshell, add their electronic spins and their orbital angular momenta separately. Label the total spin and the total orbital momentum quantum numbers by s and l, respectively. Write down the possible values spanned by s...
3. Knowing that the magnesium and aluminum atoms possesses 12 and 13 electrons respectively: (a) Write...
3. Knowing that the magnesium and aluminum atoms possesses 12 and 13 electrons respectively: (a) Write down the electron configuration (nl) of the ground state. Explain your answer. (b) We focus on the electron configuration determined in (a). Considering only the electrons from the outer subshell, add their electronic spins and their orbital angular momenta separately. Label the total spin and the total orbital momentum quantum numbers by s and l, respectively. Write down the possible values spanned by s...
Recall that the time evolution of a wavefunction y(x, t) is determined by the Schrödinger equation,...
Recall that the time evolution of a wavefunction y(x, t) is determined by the Schrödinger equation, which in position space reads iħ 4(x, t) = -24(x, t) + V(x, t)(x, t). ih vrt - h ? a) Consider any two normalized solutions to the Schrödinger equation, 41(2, t) and 02(3,t). Prove that their inner product is independent of time, doo 1 Vi (2, t)u2(x, t) dc = 0. dt J-00 Hint: prove the useful intermediate result, a 202 201 -...
6.16 The deuteron is a nucleus of heavy hydrogen consisting of ne proton and one neutron.As...
6.16
The deuteron is a nucleus of heavy hydrogen consisting of ne
proton and one neutron.As a simple model for this nucleos consider
a single particle of mass m moving in a fixed spehreical -symmetric
potencial V(r) defined by V(r)=-Vo for rro .This is called a
spherical square well potential.Asssume that the particle is in a
bound state with l=0
a) Fin the general solutions R(r) to the radical Schoringer
euatio for rro.Use the fact that the wave function must...
2. Goal of this problem is to study how tunnelling in a two-well system emerges. In particular, w...
2. Goal of this problem is to study how tunnelling in a two-well system emerges. In particular, we are interested in determining how the tunnelling rate T' of a particle with mass m scales as a function of the (effective) height Vo - E and width b of an energy barrier separating the two wells. The following graphics illustrates the set-up. Initially the particle may be trapped on the left side corresponding to the state |L〉, we are now interested...
Can someone please explain why they only considered 0,2 and 5 as their frequencies and didn't inc...
can someone please explain why they only considered 0,2 and 5 as
their frequencies and didn't include -2 and -5? Also, how did they
get the angles for the changes column? please explain with steps.
thank you
1. (i) (8 pts) The input signal z(t) to a continuous time (CT) linear time-invariant (LTI) system is given by x(t) 12 cos 2t +sin 5t The output y(t) is found to be given by y(t) 3-4 sin 2t 0.5 sin 5t At...
Question 1 (8 marks in total) The deuteron is a bound state of a proton and a neutron. Treating nucleons as identical particles with spin and isospin degrees of freedom, the total state of the deuteron can be writ- ten space Ψ spin Ψ isospin. The deuteron has a total angular momentum quantum number J - 1 and a total spin S -1. Our goal is to determine the parity of the deuteron Q1-1 (1 mark) Show that the possible...
Problem 4 Imagine that a pion π-is captured by a deuteron nucleus fron a p-orbit with spin 1 eventually converted to two neutrons through strong interaction. (a) What are the possible values of the orbital angular momentum for the neutron pair? (b) Show that the neutron should be in a spin singlet state. (c) Repeat part (a) and (b) if the deuteron is in s-state with spin 1. Hint: The parity of the deutcron is +1. Assumc that the pion...
1. (a) (10 pt) Which of the following wavefunctions CAN be a valid total wavefunction for the excited electronic state of He: 2p13d1 with the total electron spin in the triplet state (25+1 = 3), where N is the normalization constant. Explain your choice. (i) NW2p(1)3d(2) [0(1)(2)-6(1)a(2)] (ii) N [42p(1)93a(2) - za142p(2)] [a(1)B(2)+B(1)a(2)] (iii) N (42p(1)43a(2) + Y3d(1)420(2)) [a(1)$(2)-B(1)a(2)] (iv) N (42p(1)^3a(2) - 43a(1)#2p(2)] a(1)a(2) (b) (10 pt) Determine the normalization constant N in the following wavefunctigo: N [Uzo(1)3d(2) W3d(1)42p(2))...
Tl 6. (4 pts) We calculated Ahf for the ground state Hydrogen atom, but now let us consider Hht for the ground state of the deuterium atom. The basic idea is the same: Here the matrix representation of S is the same, since it represents the spin operator for the spin- electron, but that of 7 is different because the deuteron is a spin-1 particle (neutron+proton) whose spin has 3 possible values for the magnetic quantum number. Also, we must...
Recall that the time evolution of a wavefunction y(x, t) is determined by the Schrödinger equation, which in position space reads iħ 4(x, t) = -24(x, t) + V(x, t)(x, t). ih vrt - h ? a) Consider any two normalized solutions to the Schrödinger equation, 41(2, t) and 02(3,t). Prove that their inner product is independent of time, doo 1 Vi (2, t)u2(x, t) dc = 0. dt J-00 Hint: prove the useful intermediate result, a 202 201 -...
6.16
The deuteron is a nucleus of heavy hydrogen consisting of ne
proton and one neutron.As a simple model for this nucleos consider
a single particle of mass m moving in a fixed spehreical -symmetric
potencial V(r) defined by V(r)=-Vo for rro .This is called a
spherical square well potential.Asssume that the particle is in a
bound state with l=0
a) Fin the general solutions R(r) to the radical Schoringer
euatio for rro.Use the fact that the wave function must...
2. Goal of this problem is to study how tunnelling in a two-well system emerges. In particular, we are interested in determining how the tunnelling rate T' of a particle with mass m scales as a function of the (effective) height Vo - E and width b of an energy barrier separating the two wells. The following graphics illustrates the set-up. Initially the particle may be trapped on the left side corresponding to the state |L〉, we are now interested...
can someone please explain why they only considered 0,2 and 5 as
their frequencies and didn't include -2 and -5? Also, how did they
get the angles for the changes column? please explain with steps.
thank you
1. (i) (8 pts) The input signal z(t) to a continuous time (CT) linear time-invariant (LTI) system is given by x(t) 12 cos 2t +sin 5t The output y(t) is found to be given by y(t) 3-4 sin 2t 0.5 sin 5t At...
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