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is captured 5.) A deuteron d has spin 1, whereas a " has spin 0 and...
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...
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...
Ex.6 10% Consider the discussion of the determination of the parity of . Suppose that had...
Ex.6 10% Consider the discussion of the determination of the parity of . Suppose that had spin 1, but was still captured in an L = 0 orbital state in the reaction - + d 2n. What are possible two-neutron states? Which states are allowed if the had negative parity?
4. The 7 meson has spin-0, a total width T = 1.31 +0.05 keV and two...
4. The 7 meson has spin-0, a total width T = 1.31 +0.05 keV and two important decay modes: 7 + T° +7° +7° and 9 + A++ +7°. (a) (1 mark) What force dictates the decay of this particle? (b) (3 marks) Deduce the parity of the 7 meson. Show your work. (c) (2 marks) Using your answer from (b), explain why the decays n +7° +7° and n++ + + have never been observed. (d) (3 marks) Use...
ILUULLUHUJJ. U TILI JL CUILIUI " J.. 3) Two-electron system: Consider a two-electron system. The spin-orbitals...
ILUULLUHUJJ. U TILI JL CUILIUI " J.. 3) Two-electron system: Consider a two-electron system. The spin-orbitals are denoted by Wiolj = 0;\; X.;) where i is the orbital quantum number, o is the spin quantum number, r; and s; are the space and spin coordinates of the ith electron. The composite wave function is in a state given by: 114.2) 42.2 4.2) 2.2 (a) Find A. (b) Show that y 1,2 can be separated into space and spin components, i.e....
à 154 5. The example in question 4 was for a singlet state, which use spin...
à 154 5. The example in question 4 was for a singlet state, which use spin 20 2px 2px 2pz wavefunctions to impart the antisymmetry property. For triplets, the This is a 1812s1 "space" wavefunctions are used to enforce the antisymmetry triplet state property. For example, the proper antisymmetric wavefunction for a 2s'1s1 spinup-spinup configuration is: (1.2) - 92s(r.)41s(2) – 42s (r2)4s(r)) 2)915}a(1)a(2) V2 2px 2py 2pz a. Let's see what happens if the two electrons are in the same...
4 5=(1) The three Pauli spin matricas are: 0 = (d), (2 ), and show that:...
4 5=(1) The three Pauli spin matricas are: 0 = (d), (2 ), and show that: a) Fi)* = 12 z = i (bo
(L43*) Spin can be represented by matrices. Show that all three spin matrices l 0 2 0 -1 0),"2=2 1 have eigenval...
(L43*) Spin can be represented by matrices. Show that all three spin matrices l 0 2 0 -1 0),"2=2 1 have eigenvalues of +1/2h and -1/2h. Calculate the corresponding eigenfunctions which we will denote as α-and β-eigenfunctions corresponding to spin l/2 particles. Show that Sj can be determined by the commutation of the other two matrices sn and sm, n, maj. Prove that the (2×2) matrix sz-s' +ss+s, commutes with all spin matrices, ie. s2s,-sis-. Calculate the eigenvalues of s2....
Consider a particle in a 1-d well with potential V(x) =-U for-d < x < d,...
Consider a particle in a 1-d well with potential V(x) =-U for-d < x < d, and V(z) 0 elsewhere. We will use the variational wave function v(z) = A(b + r), t(x)-A(b-x), -b < r < 0, 0 < x < b, to show that a bound state exists for any U0. a) Normalize the wave function. Find the expectation values of the kinetic and potential energies b) Show that for sufficiently large b, with b> d, the expectation...
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...
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...
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...
Ex.6 10% Consider the discussion of the determination of the parity of . Suppose that had spin 1, but was still captured in an L = 0 orbital state in the reaction - + d 2n. What are possible two-neutron states? Which states are allowed if the had negative parity?
4. The 7 meson has spin-0, a total width T = 1.31 +0.05 keV and two important decay modes: 7 + T° +7° +7° and 9 + A++ +7°. (a) (1 mark) What force dictates the decay of this particle? (b) (3 marks) Deduce the parity of the 7 meson. Show your work. (c) (2 marks) Using your answer from (b), explain why the decays n +7° +7° and n++ + + have never been observed. (d) (3 marks) Use...
ILUULLUHUJJ. U TILI JL CUILIUI " J.. 3) Two-electron system: Consider a two-electron system. The spin-orbitals are denoted by Wiolj = 0;\; X.;) where i is the orbital quantum number, o is the spin quantum number, r; and s; are the space and spin coordinates of the ith electron. The composite wave function is in a state given by: 114.2) 42.2 4.2) 2.2 (a) Find A. (b) Show that y 1,2 can be separated into space and spin components, i.e....
à 154 5. The example in question 4 was for a singlet state, which use spin 20 2px 2px 2pz wavefunctions to impart the antisymmetry property. For triplets, the This is a 1812s1 "space" wavefunctions are used to enforce the antisymmetry triplet state property. For example, the proper antisymmetric wavefunction for a 2s'1s1 spinup-spinup configuration is: (1.2) - 92s(r.)41s(2) – 42s (r2)4s(r)) 2)915}a(1)a(2) V2 2px 2py 2pz a. Let's see what happens if the two electrons are in the same...
4 5=(1) The three Pauli spin matricas are: 0 = (d), (2 ), and show that: a) Fi)* = 12 z = i (bo
(L43*) Spin can be represented by matrices. Show that all three spin matrices l 0 2 0 -1 0),"2=2 1 have eigenvalues of +1/2h and -1/2h. Calculate the corresponding eigenfunctions which we will denote as α-and β-eigenfunctions corresponding to spin l/2 particles. Show that Sj can be determined by the commutation of the other two matrices sn and sm, n, maj. Prove that the (2×2) matrix sz-s' +ss+s, commutes with all spin matrices, ie. s2s,-sis-. Calculate the eigenvalues of s2....
Consider a particle in a 1-d well with potential V(x) =-U for-d < x < d, and V(z) 0 elsewhere. We will use the variational wave function v(z) = A(b + r), t(x)-A(b-x), -b < r < 0, 0 < x < b, to show that a bound state exists for any U0. a) Normalize the wave function. Find the expectation values of the kinetic and potential energies b) Show that for sufficiently large b, with b> d, the expectation...
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...
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Amplitude=3;
fs=8000;
n=0:399;
t=0:1/fs: n*1/fs-1/fs;
signal=3+3*cos(2*pi*1100*t)+3*cos(2*pi*2200*t)+3*cos(2*pi*3300*t);
fftSignal= fft(signal);
fftSignal=f ftshift (fftSignal);
f=fs/2*linspace(-1,1,fs);
plot(f,abs(fftsignal);
xlabel('Frequency(Hz)’)
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