Recent content by Axiom17

.. yes so as I thought, in that example the state wouldn't be an eigenstate of the operator. Thanks for you help with this! :biggrin:

I think it's not helping me messing up latex coding on here a bit! :shy: Let's try again.. Formula: L_z \psi_{n,l,m}(x) = \hbar m \psi_{n,l,m}(x) State - Wavefunction 1: L_{z}(\psi_{3,5,1}) = \hbar (1)\psi_{3,5,1}= \hbar \psi_{3,5,1} State - Wavefunction 2: L_{z}(-i\psi_{4,1,0})= -i...

Ok sure, good. I take it this would be the same method if I had just a '2' or a '3i' or some term like that as part of the wave function. So I have this: L_{z}(\psi_{3,5,1}) = \hbar^2 l(l + 1)\psi_{n,l,m}(x) = \hbar^2 5(5 + 1)(\psi_{3,5,1})=30\hbar^2(\psi_{3,5,1}) L_{z}(-i\psi_{4,1,0})=...

Thanks Diazona your explanation is very good :approve:. So I use this formula: L^2\psi_{n,l,m}(x) = \hbar^2 l(l + 1)\psi_{n,l,m}(x) For example: L^2\psi_{3,1,1}(x) = \hbar^2 1(1 + 1)\psi_{3,1,1}(x) = 2\hbar^2\psi_{3,1,1}(x) Therefore \psi_{3,1,1} is an eigenstate of L^{2} .. correct...

.. I thought not, but I didn't know what else to do, just thought would check that was incorrect. .. is that where you can do multiplication by multiplying each part seperately then adding the products. So the calculation is say 3x17 so can do 3x10=30 + 3x7=21 hence 3x17=30+21=51. Ok so...

ok.. but how to I do that? :confused: I don't get how to sum the two wave functions together, specifically what to do with the quantum numbers, then how to multiply that result by the operator which isn't defined. If that all makes sense. so I've got my two wave functions, p and q, and...

.. still don't understand how to do this

OK so I need to use the equation Av=av I remember that now. Let's make sure I understand, so If I have a state v which when multiplied by an operator A gives the result av where v is the input state and a is a constant, then the state v is an eigenstate of A. So in the question...

Um, sort of. But I don't get what calculations to do to show this.

Homework Statement 1. Is state \psi_{0,2,1}-\psi_{5,0,1} an eigenstate of L_{x} 2. Is state \psi_{1,3,1}-\psi_{4,2,0} an eigenstate of L^{2} Homework Equations Stationary state of Hamiltonian defined by: [itex]\psi_{n,l,m}[/tex] where the subscripts denote quantum numbers. The...

.. so P(E_{1})=\frac{E_{1}^{2}}{E_{1}^{2}+E_{2}^{2}} ? or something like that

that.. | |\psi\rangle |^{2}=E_{1}^{2}+E_{2}^{2} ?

I've still not understood this :frown:

Still don't get this :frown:

Homework Statement To determine whether two wave functions, \psi_{1} and \psi_{1} correspond to the same quantum state of a particle. Homework Equations Calculations (simplified): \psi_{1}(x,y,z)=A \psi_{2}(x,y,z)=e^{z}A The Attempt at a Solution The two wave functions do...