Homework Answers
Add Answer to:
lup)-- CI+) + I-)) I. The spin state: is an eigenvector of one of the ½ spin operators. A) Determine the operator (one...
(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....
Problem2 Two possible wave functions for two spin 1 /2 particles with Sz = 0 are Apply the operator S+ to both states as many times as needed to find the largest possible value for m and hence det...
Problem2 Two possible wave functions for two spin 1 /2 particles with Sz = 0 are Apply the operator S+ to both states as many times as needed to find the largest possible value for m and hence determine the value of S2 for each state
Problem2 Two possible wave functions for two spin 1 /2 particles with Sz = 0 are Apply the operator S+ to both states as many times as needed to find the largest possible value...
4. 10 points The Spin operators for a spin-1/2 particle can be described by the Pauli...
4. 10 points The Spin operators for a spin-1/2 particle can be described by the Pauli matrices: 0 1 0 0 ,02= 0 -1 1 ¿ a) Write the normalized eigenvectors of Oz, I+) and 1-) which are defined such that 0z|+) = 1+) and 0z1-) = -1-), as column vectors in the same basis as the Pauli matrices given above. (You can assume without loss of generality that these eigenvectors are real.) (3 pts) b) Consider an eigenvector (V)...
part A is right above part B. Both were uploaded together Write the four vectors S,...
part A is right above part B. Both were uploaded together
Write the four vectors S, S = 1/2,m) (see Problem 21(b)] in terms of , ,) and determine the eigenvalues. (a) J, J2, and J3 are commuting angular momentum operators. Show that the operator § = (ſ* Ì2) İ3, commutes with the total angular momentum j = 31 +32 +33. (This implies that commutes with J? as well.) (b) S1, S2, and S3 are commuting spin-1/2 operators. Let 5,...
I ONLY NEED HELP PARTS E AND F 2. Consider the spin representation with j =...
I ONLY NEED HELP PARTS E AND F
2. Consider the spin representation with j = 2 (in units of h). The corresponding matrices are 110 1 21 122 0 -i i ols We define J2-J12 + J22 + J32, J+ = J1 + 1J2, and J-= J1-1J2. A) (1 point) Show that 12 equals the identity matrix times jG +1), where- B) (3 points) Show that aJbic Eabe Jc for each combination a, b 1, 2,3 C) (2 points)...
A spin-1 particle interacts with an external magnetic field B = B. The interaction Hamiltonian for the system is H = gB-S, where S-Si + Sỳ + SE is the spin operator. (Ignore all degrees of freedom ot...
A spin-1 particle interacts with an external magnetic field B = B. The interaction Hamiltonian for the system is H = gB-S, where S-Si + Sỳ + SE is the spin operator. (Ignore all degrees of freedom other than spin.) (a) Find the spin matrices in the basis of the S. S eigenstates, |s, m)) . (Hint: Use the ladder operators, S -S, iS, and S_-S-iS,, and show first that s_ | 1,0-ћ /2 | 1.-1)) . Then use these...
1 2. Consider the normalized spin state To (31t) +i\L)) (2) 10 (a) Is this state...
1 2. Consider the normalized spin state To (31t) +i\L)) (2) 10 (a) Is this state lx) an eigenstate of $2 ? Is it an eigenstate of Ŝe ? (Justify your answers.) In each case, if it is an eigenstate, give the eigenvalue. (b) If the spin state is as given above, and a measurement is made of the 2-component of the angular momentum, what are the possible results of that measurement and what are probabilities of each possible result?...
PLEASE COMPLETE B) and stay tuned for my following 2 questions where I will ask part c) and d). P...
PLEASE COMPLETE B) and stay tuned for my
following 2 questions where I will ask part c) and d). Part a) has
already been posted.
The lowest energy state of a hydrogen-like atom has total angular momentum J-1/2 (from the l-O orbital angular momentum and the electron spin s 1/2). Furthermore, the nucleus also has a spin, conventionally labeled I (for hydrogen, this is the proton spin, 1 1/2). This spin leads to an additional degeneracy. For example, in the...
Exercise 1: The helium atom and spin operators 26 pts (a) Show that the expectation value...
Exercise 1: The helium atom and spin operators 26 pts (a) Show that the expectation value of the Hamiltonian in the (sa)'(2a)' excited state of helium is given by E = $42.0) (Avo ) anordes ++f63,(-) (%13-12 r) 62(e)drz + løn.(r.) per 142, (ra)]" drų dr2 - / 01.(ru) . (ra) Anemia 02.(r.)61.(r.)dr; dr2 (1) Use the approximate, antisymmetrized triplet state wave function for the (Isa)'(280)' state as discussed in class. Hint: make use of the orthonormality of the hydrogenic...
2. The ladder operators can be used to determine the lowest eigenstate (ground state) of the...
2. The ladder operators can be used to determine the lowest eigenstate (ground state) of the harmonic oscillator by using the following relation of the annihilation operator, à alo) - 0 This equation is fundamental to ladder operators and implies that it is not possible to step down further in energy than the ground state. Determine the ground state wave function h(x (i.e. [0) using the relation above and the following information The annihilation operator is defined as: ) ·The...
(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....
Problem2 Two possible wave functions for two spin 1 /2 particles with Sz = 0 are Apply the operator S+ to both states as many times as needed to find the largest possible value for m and hence determine the value of S2 for each state
Problem2 Two possible wave functions for two spin 1 /2 particles with Sz = 0 are Apply the operator S+ to both states as many times as needed to find the largest possible value...
4. 10 points The Spin operators for a spin-1/2 particle can be described by the Pauli matrices: 0 1 0 0 ,02= 0 -1 1 ¿ a) Write the normalized eigenvectors of Oz, I+) and 1-) which are defined such that 0z|+) = 1+) and 0z1-) = -1-), as column vectors in the same basis as the Pauli matrices given above. (You can assume without loss of generality that these eigenvectors are real.) (3 pts) b) Consider an eigenvector (V)...
part A is right above part B. Both were uploaded together
Write the four vectors S, S = 1/2,m) (see Problem 21(b)] in terms of , ,) and determine the eigenvalues. (a) J, J2, and J3 are commuting angular momentum operators. Show that the operator § = (ſ* Ì2) İ3, commutes with the total angular momentum j = 31 +32 +33. (This implies that commutes with J? as well.) (b) S1, S2, and S3 are commuting spin-1/2 operators. Let 5,...
I ONLY NEED HELP PARTS E AND F
2. Consider the spin representation with j = 2 (in units of h). The corresponding matrices are 110 1 21 122 0 -i i ols We define J2-J12 + J22 + J32, J+ = J1 + 1J2, and J-= J1-1J2. A) (1 point) Show that 12 equals the identity matrix times jG +1), where- B) (3 points) Show that aJbic Eabe Jc for each combination a, b 1, 2,3 C) (2 points)...
A spin-1 particle interacts with an external magnetic field B = B. The interaction Hamiltonian for the system is H = gB-S, where S-Si + Sỳ + SE is the spin operator. (Ignore all degrees of freedom other than spin.) (a) Find the spin matrices in the basis of the S. S eigenstates, |s, m)) . (Hint: Use the ladder operators, S -S, iS, and S_-S-iS,, and show first that s_ | 1,0-ћ /2 | 1.-1)) . Then use these...
1 2. Consider the normalized spin state To (31t) +i\L)) (2) 10 (a) Is this state lx) an eigenstate of $2 ? Is it an eigenstate of Ŝe ? (Justify your answers.) In each case, if it is an eigenstate, give the eigenvalue. (b) If the spin state is as given above, and a measurement is made of the 2-component of the angular momentum, what are the possible results of that measurement and what are probabilities of each possible result?...
PLEASE COMPLETE B) and stay tuned for my
following 2 questions where I will ask part c) and d). Part a) has
already been posted.
The lowest energy state of a hydrogen-like atom has total angular momentum J-1/2 (from the l-O orbital angular momentum and the electron spin s 1/2). Furthermore, the nucleus also has a spin, conventionally labeled I (for hydrogen, this is the proton spin, 1 1/2). This spin leads to an additional degeneracy. For example, in the...
Exercise 1: The helium atom and spin operators 26 pts (a) Show that the expectation value of the Hamiltonian in the (sa)'(2a)' excited state of helium is given by E = $42.0) (Avo ) anordes ++f63,(-) (%13-12 r) 62(e)drz + løn.(r.) per 142, (ra)]" drų dr2 - / 01.(ru) . (ra) Anemia 02.(r.)61.(r.)dr; dr2 (1) Use the approximate, antisymmetrized triplet state wave function for the (Isa)'(280)' state as discussed in class. Hint: make use of the orthonormality of the hydrogenic...
2. The ladder operators can be used to determine the lowest eigenstate (ground state) of the harmonic oscillator by using the following relation of the annihilation operator, à alo) - 0 This equation is fundamental to ladder operators and implies that it is not possible to step down further in energy than the ground state. Determine the ground state wave function h(x (i.e. [0) using the relation above and the following information The annihilation operator is defined as: ) ·The...
Most questions answered within 3 hours.
-
Part 1. Primitive Types, Sorting, Recursion for
Homework.java
a) Implement the static method initializeArray that receives...
asked 51 minutes ago -
Using C++, build a sorter that can rank a sequence of numbers in
a descending order....
asked 47 minutes ago -
Derive ground state term symbols. Use notation 2S(1/2) for state
2S1/2
a) d5
b) f3
c)...
asked 1 hour ago -
A sample of size 31 will be drawn from a population with mean 39
and standard...
asked 1 hour ago -
What is the effect on the P-value when a test is changed from a
two-tailed hypothesis...
asked 1 hour ago -
I wish to estimate µ, the mean of a population. After I collect
and an-
alyze...
asked 2 hours ago -
At a local university, you poll a group of 115 students and find
that 37 of...
asked 2 hours ago -
Gladstone company tracks the number of units purchased and sold
throughout each accounting period but applies...
asked 2 hours ago -
When determining if a molecule's configuration is E or Z, what
determines the higher priority groups?
asked 2 hours ago -
13. What is the amount
of conversion cost transferred to finished goods? (Round
your intermediate calculations...
asked 2 hours ago -
Sulfuric Acid is a "strong" acid, but only releases a single
proton when it dissolves. What...
asked 2 hours ago -
The
second floor of a house is 6 m above the street level. How much
work...
asked 2 hours ago