Show by direct evaluation that the eigenvectors of Pauli\'s sigma_y matrix (in t
ID: 3840434 • Letter: S
Question
Show by direct evaluation that the eigenvectors of Pauli's sigma_y matrix (in the representation of the eigenvectors |+| and | rightarrow of sigma_x) |+, > = 1/Squareroot 2 (1 i); |-, > = 1/Squareroot 2 (1 -i) satisfy the relations S_y| + > = 1/Squareroot 2 (1 i); | rightarrow = 1/Squareroot 2 (1 -i) satisfy the relations S_y |+_y) = h/2|+_y) S_y |-_y] = h/2 -_y) where S_y = h/2 (0 -i i 0) is the y-component of the 1/2-spin operator in the same representation. That is, show that |+_y> and |-_y) are eigenvectors of S_y with eigenvectors plusminus h/2 (b) Give the numerical value of h/2 in J-s/mol units, and (c) show that the SI units of position times liner momentum are also J-s. Find the probability to measure S_x = +h/2 in: (a) a 1/2-spin beam of particles polarized along the y direction with quantum state |+_y) = 1/Squareroot 2 |+0 + i/Squareroot 2} -) and (b) in 1/2-spin beam of particles polarized in xz plane along an axis at an angle theta = 45 degree relative to the z axis, with quantum state |Psi_theta| = cos theta/2 |+| + sin theta/2| rightarrow Express probabilities in percent units. (c) Using linear algebra operations, find the expectation value of the spin the z axis for the quantum state in (b (S_z)_theta = Psi_theta| S_z|Psi_theta| where S_z = h/2 (1 0 0 -1) Express the result in SI units. (d) Confirm that the result in (c) is consistent with the weighted average of the spin up and spin down states along the z axis; |S_z|_theta = h/2 p, + (h/2) p. where p_1 and p_2 are respectively, the probabilities to measure S_x = +h/2 and S_z = -h/2 in the quantum state in(b).Explanation / Answer
1. Answer
Option a is true it is so because method 1st has name findAnswer and its two parameters as a String and int type and method 2nd also has same name and same parameters in same sequence (i.e., First a String and 2nd an int). Hence this option is correct. Please note that name and sequence of parameters type must be same for the methods to call them as having same signature, however parameters' variable names can be different.
2. Answer
Completed Java Code
public class PiggyBank {
public PiggyBank()
{
nickels = 0;
dimes = 0;
quarters = 0;
}
public void addNickels(int count)
{
nickels = count ;
}
public void addDimes(int count)
{
dimes = count ;
}
public void addQuarters(int count)
{
quarters = count ;
}
public double getTotal()
{
return (nickels*Nickel_value) + (dimes*Dime_Value) + (quarters*Quarter_Value);
}
public void subtractDimes(int count)
{
if(dimes >= count)
dimes = dimes - count;
else
System.out.println("Cannot subtract dimes! Insufficient Dimes in the Piggy Bank!");
}
private static final double Nickel_value = 0.05;
private static final double Dime_Value = 0.1;
private static final double Quarter_Value = 0.25;
private int nickels;
private int dimes;
private int quarters;
}