Binomial Expansion: Solve for L=Hbar*(l+1/2)

In summary, the individual is trying to solve a problem involving the equation L = Hbar * √(l*(l+1)). They provide a link to a previous post where they obtained the equation L = Hbar * (l + 1/2), and they believe the two equations are equivalent. However, when plugging in specific values for l, the two equations do not give the same result. The individual asks for help in understanding why this is the case.
  • #1
perplexabot
Gold Member
329
5
Hey all. I have posted a thread regarding this question a while back. I did get an answer and everything. (Here is my old post along with the original question if you are interested: https://www.physicsforums.com/showthread.php?t=592885).

So i tried doing that problem again like this:

Given:
L = Hbar * √(l*(l+1))
Binomial expansion approximation: (1+z)^n = 1 + nz

My try:
L = Hbar * √l * (1 + l/2)

If you opened the link of my previous post you will see that I must obtain L = Hbar * (l + 1/2). As you can see my just calculated expression is not the same as the previous expression, however plugging in a certain value of l, one obtains the same value for either expression which leads me to believe the two expressions are equivalent. So my question is: How would I play with my current equation to obtain the equation from the previous post. Yes, this is completely an algebra question. Thank you.
 
Last edited:
Physics news on Phys.org
  • #2
I'm going to call your lower-case l capital L because l looks like 1.

Hbar * √(L*(L+1)) is not equal to Hbar * √L * (1 + L/2), if that is what you are claiming? To see this, just plug in L = 1. Then the first expression becomes hbar*sqrt(2) while the second becomes hbar * (3/2).

Nor is Hbar * √L * (1 + L/2) equal to Hbar * (L + 1/2), if that is what you are claiming. Just plug in L = 2; then the first expression is hbar * sqrt(2) * 2 while the second is hbar * 5/2.
 
  • #3
Oh, i made a stupid mistake i guess. Thank you for your correction. Can you explain why the two equations are not equivalent? I got both of them from the same equation but they are not equal.
 

Related to Binomial Expansion: Solve for L=Hbar*(l+1/2)

1. What is binomial expansion?

Binomial expansion is a mathematical process used to expand an expression with two terms raised to a power. It follows the pattern of (a+b)^n, where a and b are constants and n is a positive integer.

2. What is the formula for binomial expansion?

The formula for binomial expansion is given by (a+b)^n = ∑(nCr)a^(n-r)b^r, where n is the power, r is the term number, and nCr represents the combination of n things taken r at a time.

3. How do you solve for L in the equation L=Hbar*(l+1/2)?

To solve for L, you need to first distribute the Hbar to the terms inside the parentheses. This will give you L=Hbar*l+Hbar*(1/2). Then, subtract Hbar*(1/2) from both sides to isolate Hbar*l. Finally, divide both sides by Hbar to get the value of L.

4. What is the significance of L=Hbar*(l+1/2) in quantum mechanics?

This equation is known as the Bohr-Sommerfeld quantization condition and it helps to determine the quantized energy levels of a particle in a quantum system.

5. Can binomial expansion be used for expressions with more than two terms?

Yes, binomial expansion can be extended to expressions with more than two terms using the multinomial theorem. This theorem follows a similar pattern as the binomial theorem, but with more terms and coefficients to account for the additional variables.

Similar threads

Replies
4
Views
1K
Replies
14
Views
1K
  • Quantum Physics
Replies
17
Views
910
  • Quantum Physics
Replies
31
Views
4K
Replies
0
Views
530
Replies
3
Views
635
  • Quantum Physics
Replies
3
Views
1K
Replies
3
Views
929
Replies
6
Views
930
Replies
5
Views
2K
Back
Top