Harmonics Definition and 264 Threads

In solving the 3D hydrogen atom, we obtain a spherical harmonic, Y such that, Y_{lm}(\theta,\phi) = \epsilon\sqrt{\frac{(2l+1)}{(4\pi)}}\sqrt{\frac{(l-|m|)!}{(l+|m|)!}}e^{im\phi}P^m_l(cos \theta) where \epsilon = (-1)^m for m \geq 0 and \epsilon = 1 for m \leq 0 . In quantum, m = -l...

Ok, I was given a question in homework and was never told the right answer. If the Fundamental Frequency = 15Hz, the 3rd Harmonic = ? I estimated it at 45Hz because of an example The example was; Harm 1 = 100 x 1 = 100Hz Harm 2 = 100 x 2 = 200Hz Harm 3 = 100 x 3 = 300Hz If so...

I understand that harmonics are integer multiples of a fundamental frequency. Also, that the relative strengths of the harmonics are what make the same note on different instruments sound different. Why are these other frequencies made? How many integer multiples are there? Why do our...

I have recently come across the subject of harmonics in my new job and I am a little puzzled about them. I understand that they are produced by devices which draw current in a non-linear fashion and that they can travel throughout a network causing items to overheat and such like. BUT... I...

There is this excersise in Griffith's QM text that I can't seem to solve. It's about the calculation of the normalization factor of the spherical harmonic functions using the angular momentum step up operator. These definitions/results are given: Y_l^m = B_l^m e^{im\phi} P_l^m (\cos\theta...

So let us assume we have the following system. A harmonic oscillator consists of a mass 1g on a spring. Its frequency is 1 Hz and the masses passes through the equilibrium position with a velocity of 10cm/s. I have already calculated that the magnitude of the quantum number (n = 7.6 x 10^27)...

Complex waves... I have learned that with a musical instrument you set up standing waves of the fundamental frequency as well as other harmonics which cause the specific "quality" of the sound - my question is why do you produce different harmonics and not just the fundamental frequency? When...

Hello, My question is fairly simple. My instructor solved in class today Laplace's equation in spherical coordinates which resulted in spherical harmonics. I have not taken any quantum mechanics yet so this is my first exposure to spherical harmonics. What do the "l" and "m" terms in the...

Hi We just did a lab on waves and one in particular I'm unsure about. We set up standing waves on a spring and observed the period of each successive harmonic. It was found that the period was cut in half with each harmonic. Or the frequency was doubled. ie. harmonic 1 produced one...

Greetings, I´m calculating cuadratic dispersion of some quantum systems. I need to expand x^2 in terms of spherical harmonics (using Clebsch-Gordan coefficients, or threeJ as well) in order to be able to use Gaunt espression in the integral solving. I start from the expansion of x as...

so IN THEORY, there should be an oscillation pattern that yields the hydrogen spectrum ?

Viva! I wonder if anyone could explain me the difference between real spherical harmonics (SH) and complex SH. What's the difference in doing an expansion in either situations? And what are the orthogonality relations for each case? Any help would be great...( websites, books..)...

Dear Members of Physics Forums Cosmology Let me introduce myself. My name is Ray Tomes and after a career in computer software development and computer modelling I have spent about 15 years in full time study of cycles in many different disciplines including astronomy, geology, biology...

Can someone explain to me precisely what harmonics are, and the technical differences between even and odd numbered harmonics?