Finding E, L and Lz from wavefunction

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Homework Help Overview

The discussion revolves around a quantum mechanics problem involving the wavefunction of a hydrogen atom. Participants are tasked with finding the probabilities associated with specific quantum numbers: energy (E), angular momentum squared (L²), and the z-component of angular momentum (Lz).

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster expresses uncertainty about the equations needed to determine the probabilities of the specified quantum numbers. Some participants discuss the nature of the wavefunction as a superposition of stationary states and the implications for measurement outcomes.

Discussion Status

Participants are exploring the probabilities of collapsing into specific stationary states upon measurement. There is an exchange of ideas regarding the probabilities associated with each state, although no definitive consensus has been reached on the exact values.

Contextual Notes

The problem context includes the assumption that the wavefunction is a superposition of two stationary states, which influences the interpretation of measurement probabilities. The original poster's inquiry reflects a common challenge in quantum mechanics regarding the understanding of superposition and measurement outcomes.

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Homework Statement


We were given the wavefunction for a hydrogen atom (ignoring spin) as shown in the link below
We are asked to find the probability of obtaining E=E1, L^2=2 hbar^2 and Lz=hbar


Homework Equations


http://s633.photobucket.com/albums/uu58/john_sharkey/?action=view&current=equation.jpg


The Attempt at a Solution


i have no idea what equations i would need to find the probabilities of finding these results.
If somebody could point me in the right direction it would be much appreciated.
 
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That wavefunction is a superposition of two stationary states, namely psi_100 and psi_211. Each stationary state has a definite E, L^2, and Lz: if you know that a particle is in the state psi_100, for example, you will always get E1 when you measure its energy.

This particle is not yet in any state, but when you take a measurement, it randomly collapses into one of the two stationary states. The question is essentially asking what the probability of it collapsing into the state with energy E1 is, and ditto for L^2 and Lz.
 
is the probability of obtaining each stationary state just 2/3 and 1/3 respectively?

Also thank you very much for your help
 
Yup, and you're welcome.
 

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