Sakurai 3.5.37: Formula for Matrix Element <j m | S^2_+ |j m >

In summary, Sakurai 3.5.37 is an equation found in the book "Modern Quantum Mechanics" by Jun John Sakurai, commonly used in the field of quantum mechanics. The formula for Matrix Element <j m | S^2_+ |j m > is given by S^2_+ = S^2 - S_z^2 + S_z, and it represents the expectation value of the total spin operator squared in a specific quantum state. It is calculated using the formula <j m | S^2_+ |j m > = ħ^2j(j+1) - ħ^2m^2 + ħm, and it is important in quantum mechanics for predicting and understanding various
  • #1
760
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Does anyone know what the formula is for the following:

<j m | S^2_{+} |j m > = ?

Reference to equations in Sakurai would be helpful in deriving the relation. I would suspect 3.5.37 but what about the delta_j j' ?

Does anyone know what I'm talking about?
 
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  • #2
3.5.35 a

<j',m|J^2 |j,m> = j(j+1)hbar^2 delta_j j' delta m m'

3.5.37 is

J_+ |j,m> = c_jm^+ |j,m+1>
 
  • #3
These appear to be formulas for finding the spin, and or angular momentum, of a wave-function. What is your question exactly?
 
  • #4
nevermind.
 

What is Sakurai 3.5.37?

Sakurai 3.5.37 refers to a specific equation in the book "Modern Quantum Mechanics" written by Jun John Sakurai, which is commonly used in the field of quantum mechanics.

What is the formula for Matrix Element ?

The formula for Matrix Element is given by:
S^2_+ = S^2 - S_z^2 + S_z (where S^2 is the total spin operator and S_z is the z-component spin operator).

What does the Matrix Element represent?

The Matrix Element represents the expectation value of the total spin operator squared in a specific quantum state, with j representing the total spin quantum number and m representing the z-component spin quantum number.

How is the Matrix Element calculated?

The Matrix Element is calculated using the formula:
= ħ^2j(j+1) - ħ^2m^2 + ħm (where ħ is the reduced Planck's constant).

Why is the Matrix Element important in quantum mechanics?

The Matrix Element is important in quantum mechanics because it represents the total spin of a particle, which is a fundamental property in the quantum world. It is also used in calculations and predictions of various physical phenomena, such as atomic and molecular structures, and nuclear reactions.

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