# How Does Feynman Normalize CII in the Ammonia Molecule States?

• harpf
In summary, Feynman's explanation on page 9-3 of Volume 3 of The Feynman Lectures on Physics states that if CII = <II|Φ>, then you can substitute it for both <II|1> and <II|2>. To go further, you may need to use C1 = C2 and possibly C1*, and <2|1> = <1|2> = 1/2.
harpf
I'm trying to follow Feynman's explanation on page 9-3 of Volume 3 of The Feynman Lectures on Physics. I've attached a copy of the section in question.

To normalize CII he notes that
< II | II > = < II | 1 >< 1 | II > + < II | 2 >< 2 | II > = 1
I am not clear how he derives the conclusion
CII = 1/√2 (C1 + C2)

I tried to solve the first equation unsuccessfully like this-
< II | 1 >< 1 | II > + < II | 2 >< 2 | II > = 1
CII C1 + CII C2 = 1
[1/√2 (C1 + C2)] C1 + {1/√2 (C1 + C2)} C2 = 1
[1/√2 (C1 + C2)] (C1 + C2) = 1
1/√2 (C1 + C2) (C1 + C2) = 1
which isn’t working for me.

Thank you for clarifying.

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The step from the first to the second line of your attempt is wrong. You've lost half of the matrix elements.

Thank you for your response, M Quack, which is clear and helpful.

If CII = < II | Φ >, I’m assuming I can substitute it for both < II | 1 > and < II | 2 >. You can see I’ve taken the same approach with C1 and C2. I suspect to go further I may have to use C1 = C2 and possibly C1*, which I am frankly weak on, and < 2 | 1 > = < 1 | 2 > = 1 / 2.

The source of my confusion may be a basic misunderstanding of state transitions and the meaning of the coefficients, C1, C2, and CII. I am really struggling to move forward. Thank you.

<ii | 1> <1 | ii> = (cii^* c1) (c1^* cii)

= (1/√2 (c1+c2)^* c1) (c1^* 1/√2 (c1+c2)
= 1/2 (c1^* c1 + c2^*c1) (c1^*c1+c1^*c2)
= 1/2 (1 + 0) (1 + 0)

Do you see what I mean when I say you dropped half the matrix elements?

That’s really helpful. The fog begins to lift. Thanks again.

I now realize the difference between < II | Φ >, which is CII, and < II | 1 >, which is the product of | 1 > and < II |.
Also, < II | = | II >* = CII*.

No, I can’t say I see what you mean about the matrix elements (although implying I was able to identify half of them seems generous).

<II|i> is nothing else than a matrix element between the old and new wave functions. Maybe that is speaking a bit loosely as usually a matrix element is <x|M|x> where |x> is the wave function or state, and M some operator or matrix, depending on the notation.

## 1. What are Feynman ammonia molecule states?

Feynman ammonia molecule states refer to the different energy levels or quantum states that an ammonia molecule can exist in, as described by the quantum mechanics theory developed by physicist Richard Feynman.

## 2. How many states can an ammonia molecule have?

An ammonia molecule can have a total of 9 states, with 3 rotational states, 3 vibrational states, and 3 electronic states.

## 3. What is the significance of Feynman ammonia molecule states?

The concept of Feynman ammonia molecule states is important in understanding the behavior and properties of ammonia molecules, as well as in the study of quantum mechanics and molecular spectroscopy.

## 4. How are the different states of an ammonia molecule determined?

The states of an ammonia molecule are determined by the energy levels of its constituent atoms and the interactions between them, as described by the Schrödinger equation.

## 5. Can the states of an ammonia molecule be changed?

Yes, the states of an ammonia molecule can be changed through the absorption or emission of energy, such as through collisions with other molecules or exposure to electromagnetic radiation.

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