Hey Levis2! I understand your passion for mathematics - I have a similar one as well! I took Calculus BC last year (in 10th grade) and now I'm taking linear algebra and multivariable calculus as a junior. Differential equations is one of my favorite subjects in calculus and I'm hoping to either...
Ok. Thanks! So I can equate the wave functions for the x < -a to the -a < x < a regions first; then equate the wave functions for the -a < x < a and the x > a regions right? And it's perfectly fine of the factors e^(ka) and e^(-ka) remain there right?
No problem! LOL yeah, I was also confused - why for bound states, one of the terms blew up, and why for the scattering states, both e^(ikx) AND e^(-ikx) terms were kept, even though x tended to negative infinity.
Homework Statement
Consider the double Dirac delta function V(x) = -α(δ(x+a) + δ(x-a)). Using this potential, find the (normalized) wave functions, sketch them, and determine the # of bound states.
Homework Equations
Time-Independent Schrodinger's Equation: Eψ = (-h^2)/2m (∂^2/∂x^2)ψ +...
Ah ok. Thanks! LOL I was getting confused. So the reason why it doesn't "blow up" as we would expect it to is because for complex exponentials, as x -> infinity, e^(ikx) and e^(-ikx) don't blow up? Actually, that kinda makes sense because e^ix is like going in a circle in the complex plane...
In Griffith's Introduction to Quantum Mechanics, on page 56, he says that for scattering states
(E > 0), the general solution for the Dirac delta potential function V(x) = -aδ(x) (once plugged into the Schrodinger Equation), is the following: ψ(x) = Ae^(ikx) + Be^(-ikx), where k = (√2mE)/h...
I have a question: is there any way to accurately "visualize" the phenomenon of electron degeneracy pressure? I understand that the main concept behind it is the Pauli Exclusion Principle. However, I was reading about the Chandrasekhar limit, and that it's derived from the fact that although a...
How to find the "mass-energy" in a certain field
I saw somewhere that for a charged particle of radius R, the method of finding the "mass-energy" in such an electrostatic field (caused by the charged particle is)
M = ∫E^2 dV, where E is the electric field of the particle, and the bounds of...
Right. Ok. Sorry, I got a bit confused there. I'm just studying quantum mechanics so I'm not familiar with nuclear binding energy, the mechanics of fusion, and stellar stuff in general. Thanks for clarifying!
Thanks! So it basically takes more energy to fuse Fe into heavier elements than the energy available from previous fusion events. Ok, that makes sense. Thanks!