Hydrogen atom radial wavefunctions
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- เผยแพร่เมื่อ 20 ก.ค. 2024
- The hydrogen atom radial wavefunctions are derived by change of variables, removal of asymptotic dependence, and power series. Normalizability of the wavefunction requires termination of the power series, leading to energy quantization. (This lecture is part of a series for a course based on Griffiths' Introduction to Quantum Mechanics. The Full playlist is at th-cam.com/users/playlist?list=...)
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Excellent supplement to Griffiths. Thank you.
Griffiths skips so many crucial steps and explanations in this section. Thanks for making this video, helped me a lot.
Its not just the griffiths, every litterature i found on this subject skipped the crucial steps. I'll never understand why
What's the crucial steps?
I thought it was completely over in this class, then I saw your videos. thanks a bunch
The greatest lecture of all time
Thank you so much for these well explained quantum mechanics videos. It is incredibly helpful.
I think this will save my final grade! thank for sharing this on youtube. very helpful
Hey Prof, your radial graph of n=3 and l=0 at time point 46:47 (green curve) does not match the Griffiths radial function n=3, l=0. Griffiths page 141 shows that n=3 and l=0 crosses the x-axis more often than yours. Are the graphs not supposed to be the same? Figure 4.4 in Griffiths.
Are there solutions to your "check your understanding" questions anywhere? Apologies if I've missed this info in one of your videos +Brant Carlson
Sir, many thanks for making me unerstand the asymptotic behaviour .
At around 40:45. Isn't it supposed to be n-2l-1 in the subscript according to the definition?
I just have a question about the recurrence relation. For the QHO, you were able to set K = 2n + 1, so the numerator turned from 2j + 1 - K into -2(n - j.) In this problem, p_0 = 2n. For the this recurrence relation, would we keep the numerator as 2(j + l + 1) - p_0, or make it 2( j + l + 1 - n)? Thank you
great sir. i am fallowing u excellenct
Thank you!!
Wow , it made the lecture i just had more understandable.
i love you for this thank you
I am sorry for the dumbness, but I didn't understand where did the Bessel associated functions go.
+Pedro Torres That was for the spherical barrier problem. A more trivial case he demonstrated as a (not very realistic) example.
I don't understand the part where you have two definitions on dv/dp where the indicies are offset by 1. I agree you can use either definition as long as you stick to one form only. But when you do the second derivative, you use both form of indices definitions in one expression. Is that ok? I don't get it. It is like my boss shifting the decimal point on my salary to the left by one place.
Hello. Thank you for your lecture. I have a question: why is it not allowed to let the wave function blow up near 0?
Because it doesn't make any physical sense, often in electrodynamic we came across such cases and there we choose the constant as zero.
why did you change exp(rho) to exp(-rho) from where the minus came
+Zniber Mohammed from the asymptotic form rho -> infinity => u = Aexp(-rho) because the Bexp(rho) blows up
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39:36 I get why j_max is an integer but what about l?
Go back and watch/read the section on spherical harmonics. We found that l must be a positive integer from the differential equation who's solutions are the associated Legendre polynomials. I hope this helps!
6:11 how could a function of r be = to a function of kr?
is this is the part of jee syllabus
41:13 The subscript for the associated Laguerre polynomial is q+p NOT q-p. Common rookie mistake!
I think not, look at the book again where it is defined {L^p}_q