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

• Nusc
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

Nusc

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?

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>

These appear to be formulas for finding the spin, and or angular momentum, of a wave-function. What is your question exactly?

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.