Deriving the L+-L- Formula in Quantum Mechanics

In summary, the conversation is about a quantum mechanics problem and the derivation of a formula. The problem statement involves deriving the formula L+-L- =-(h/2π)^2[d²/dθ²+cotθ d/dθ +cot²θ d²/dθ²+id/dφ] from the formula L+-L-=±(h/2π)e^±(iθ)[d/dθ + i cotθ d/dφ]. The person asking for help is unsure of how to approach the problem and is looking for suggestions. The conversation concludes with them realizing their mistake and thanking for the help.
  • #1
venusfly
2
0
Hello, I have a quantum mechanics problem. Here is the problem statement. I must derive this formula,

L+-L- =-(h/2π)^2[d²/dθ²+cotθ d/dθ +cot²θ d²/dθ²+id/dφ]

from this formula,

L+-L-=±(h/2π)e^±(iθ)[d/dθ + i cotθ d/dφ]

I have no idea how to approach this problem. Can anyone give me a suggestion on how to begin the proof? Thanks.
 
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  • #2
Something is wrong here: L+-L- can't be equal to both! The first is clearly a second derivative. Is it supposed to be something like (L+-L-)2?
 
  • #3
Done

Sorry, wrote it wrong. Got the answer though. Thanks.
 

1. What is quantum mechanics derivation?

Quantum mechanics derivation is the mathematical process of deriving the fundamental principles and equations that describe the behavior of particles and energy at the quantum level.

2. How is quantum mechanics derivation related to classical mechanics?

Quantum mechanics derivation is a more comprehensive and accurate theory than classical mechanics, as it accounts for the behavior of particles and energy at the quantum level. It can be seen as an extension of classical mechanics to the microscopic world.

3. What are the key principles involved in quantum mechanics derivation?

The key principles involved in quantum mechanics derivation include the wave-particle duality, uncertainty principle, superposition, and entanglement.

4. What are the most commonly used equations in quantum mechanics derivation?

The most commonly used equations in quantum mechanics derivation include the Schrödinger equation, Heisenberg's uncertainty principle, and the Pauli exclusion principle.

5. How is quantum mechanics derivation used in practical applications?

Quantum mechanics derivation has been applied to various fields, such as chemistry, electronics, and nanotechnology. It has also led to the development of technologies like transistors, lasers, and MRI machines.

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