Harmonics Definition and 264 Threads

Hello, I am looking for some direction to books or papers which may help me, When you solve the Helmholtz equation you end up with vector spherical harmonics as solutions. The Helmholtz equation is invarient under rotations which means that rotations of these solutions are also solutions...

1. Problem: I have a wave function ψ(r) = (x + y + z)*f(r) and want to find the expectation values of L2 and Lz. It is suggested that I first change the wave function to spherical coordinates, then put that in terms of spherical harmonics of the form Yl,m. 2. Homework Equations ...

Hello, Question is about equation 5.71 ---to-----5.72 All that was done is algebra or trigonometry? Where do I find such more example or reading or exercises. I apologize for not printing the actual equations, there were too many symbols in them. Thanks.

When solving for the spherical harmonic equations of the orbital angular momentum this textbook I'm reading.. Does this mean that there must be a max value of Lz which is denoted by |ll>? Normally the ket would look like |lm>, and since m is maxed at m=l then |ll> is the ket consisting of the...

I did an experiment for school, and I put a speaker in a styrofoam box with a rectangle cut out of the front. I had styrofoam bricks that fit perfectly in the hole, each with a hole cut out. The hole shape differed, with things like a funnel, a diagonal line, a circle, a square, etc. I was...

Electrical Engineering problems! Linear & switching mode power regulators: 1. What is the major weakness of a Buck Regulator that compared with a Linear Regulator? Is't efficiency? Passive harmonics filter: 1. If the filter reactance for harmonics is a negative value, what is...

Hello The energy of harmonics oscillator, started of U=-\frac{\partial}{\partial \beta} \ln Z is equal to \frac{\hbar \omega}{2} + \frac{\hbar \omega}{exp(\beta \hbar \omega)-1}. At high temperature, i could say that exp (\beta \hbar \omega ) \approx 1 + (\beta \hbar \omega ), and then...

Hello, Is it true that when using transformers and three-phase drives/VFDs for induction motors, the transformer's power needs to be much higher (e.g. +40%) than the drive's in order to avoid increased harmonics (or even other problems)? If you know any official standard, paper or...

Is it possible to express (cos(\theta)sin(\theta))^2 in terms of spherical harmonics?

I am trying to show that \[ Y_{\ell}^m(0,\varphi) = \delta_{m,0}\sqrt{\frac{2\ell + 1}{4\pi}}. \] When \(m = 0\), I obtain \(\sqrt{\frac{2\ell + 1}{4\pi}}\). However, I am not getting 0 for other \(m\). Plus, to show this is true, I can't methodically go through each \(m\). How can I do this?

is there an approximation for spherical harmonics for very large l and m in closed form?

Homework Statement The question is about page 198 of Jackson's Classical Electrodynamics. The magnetic scalar potential is set to be: Phi = ∫ (dΩ' cosθ'/ |x-x'|). Using the spherical harmonics expansion of 1/|x-x'|, the book claims that only l=1 survives. I...

I'm trying to better understand this circuit: https://www.circuitlab.com/circuit/qnxkke/lc-chopper/ and how the added inductors (L3, and L4) and Capacitor create a harmonic. I fully understand how to calculate the resonance for the main circuit but how would I calculate the harmonic that the...

Hi, I'm a little confused about how to apply the real spherical harmonics when building a hydrogen wave function. I'm doing a computational project, so I want to work with a wave function which is strictly real, and I'm hoping I can do so by building the orbitals using the real spherical...

Hi guys! I was wondering if anyone knew of a particularly nice book that taught one how to solve physics problems that need the use of green's functions and/or spherical harmonics. I can't seem to find a book that actually does this other than Jackson but I'd rather not tread there (I'm guessing...

Hi I am working on a optimization problem involving vector fields. In order to define a objective function I need a measure (scalar quantity) of some properties of the vector field. The vector field comes from a finite element analysis, that is the vector field is calculated on a discretized...

Homework Statement Consider 2 conductor spherical shells of radii a and b (where a>b). The inner shell is at zero potential and the outer shell is at a potential given by ##V(\theta, \phi )=V_0 \sin \theta \cos \phi ## where ##V_0## is constant and theta and phi are the usual spherical...

Why is it that we accept triple-n harmonics in the output voltage spectrum of VSCs? Assume we are using SPWM where the frequency modulation index is selected to be a large odd integer multiple of 3. Thanks again!

Hi all, I'm studying the spherical harmonics, specifically the zonals (set m=0). With the equatorial harmonics(set m=l), the classical limit is pretty darn clear; the particle just accumulates to a Dirac delta along the equator, but I've proven that the zonals don't converge to a Dirac Delta at...

This is what I tried doing, but I ended up getting an answer that isn't listed above 1. frequency = speed/wavelength 2. On Earth 480 Hz = (343 m/s)/wavelength wavelength = 343 / 480 wavelength = 0.714 is the wavelength for the Coke bottle 3. On Earth 2 Since they already gave me...

The frequency of the highest note on the saxophone is 1,568 Hz. 1.How many harmonics of that note can we hear? 2.How many harmonics of the note one octave below it can we hear? I didn't put the title in correctly on my first thread, so calm down everyone. But my book aint helping me much...

$$ Y_{\ell}^m = \sqrt{\frac{(2\ell + 1)(\ell - m)!}{4\pi(\ell + m)!}}P^m_{\ell}(\cos\theta)e^{im\varphi} $$ For ##\ell = m = 1##, we have $$ \sqrt{\frac{(2 + 1)(0)!}{4\pi(2)!}}P^1_{1}(\cos\theta)e^{i\varphi} = \frac{1}{2}\sqrt{\frac{3}{2\pi}}e^{i\varphi}\sin \theta $$ But Mathematica...

$$ Y_{\ell}^m = \sqrt{\frac{(2\ell + 1)(\ell - m)!}{4\pi(\ell + m)!}}P^m_{\ell}(\cos\theta)e^{im\varphi} $$ For $\ell = m = 1$, we have $$ \sqrt{\frac{(2 + 1)(0)!}{4\pi(2)!}}P^1_{1}(\cos\theta)e^{i\varphi} = \frac{1}{2}\sqrt{\frac{3}{2\pi}}e^{i\varphi}\sin \theta $$ But Mathematica is telling...

Homework Statement An electron in a hydrogen atom is in a state described by the wave function: ψ(r,θ,φ)=R(r)[cos(θ)+eiφ(1+cos(θ))] What is the probability that measurement of L2 will give 6ℏ2 and measurement of Lz will give ℏ? Homework Equations The spherical harmonics The...

Homework Statement Hi I have two problems i need to solve mainly 1, but i need to check if 2a and 2b is correct here it is: A simple harmonics oscillator has an amplitude of 0,1m.At what displacement will its kinetic and potential energies be equala) What is the force due to the atmosphere...

Hi, I am looking to use the definition from WGS84 to calculate Earth's gravitational potential using spherical harmonics, however I am having some difficulty finding the definition of one of the variables. Gravitational potential is given as the following: V = \frac{GM}{r}\left [ 1 +...

Hi everyone! I was reading up on sound waves and I got to the point where this website was describing how instruments produce standing waves through the interference of different frequencies but then it started to talk about how the length of air columns can affect the wavelengths of the sound...

I made a pan flute that has 1 open end and 1 closed end, so when i blow into it, the fundamentral frequency I put actually generates harmonic freqeuncies of 2f,3f,4f... and this creates distortions? Is this correct? If so, why most musical intruments don't have any distortions and sound nice? Is...

If electric waveforms such as square waves, sawtooth waves, and triangle waves are really no more than sine waves with added harmonics, one could run such a wave through a bandpass filter (or several) and isolate one of the harmonics as a sine wave?

How do you accurately identify the fundamental harmonic if you get a peak of similar amplitudes at frequencies that are really close to each other. And furthermore, once you identify the fundamental harmonic, are the second, third fourth harmonics just multiples of the fundamental frequency...

If I have a oscillator that has an infinite number of harmonics, what decides which harmonics are excited? Is it whatever frequency inputs I drive into the system, and the system damps out frequencies that don't match the harmonics or is it possible that driving at only one harmonic frequency...

Homework Statement http://img109.imageshack.us/img109/1065/87070684.png Homework Equations 1) L_{\pm}=\pm\hbar e^{\pm i \phi}(\frac{\partial}{\partial\theta}\pm i cot\theta \frac{\partial}{\partial\phi}) 2) L_{\pm}Y^m_l = \hbar\sqrt{(l \mp m)(l \pm m+1)}Y^{m \pm 1}_{l} 3)Answer...

"Harmonics in polyphase power system" Dear All, I have a problem in understanding how the harmonic currents exist in a load with no corresponding harmonic voltages? The following figures with questions under explain what I mean This understood figure no issues about. In above figure, 2...

Homework Statement A spring (spring constant=2500N/m) is fixed vertically to the floor. A 10-kg ball is placed on the spring, pushed down 0.5m, and released. How high does the ball fly above its release position?Homework Equations x=Xo cos wt w= √(k/m) T=2pi√(m/k) The Attempt at a Solution...

Fourier analysis of a square wave shows that it is made up of sine waves which are harmonics of the square wave. What I am wondering is how far do these harmonics extend to? Are they all of the same amplitude? And, can specific harmonics be filtered using a series or parallel RC filter?

What's the difference in the representation of spherical harmonics and the orbitals themselves? they look exactly the same to me... unlike the radial part of the wavefunction though.

Homework Statement An a.c. voltage, V, comprises of a fundamental voltage of 100V rms at a frequency of 120Hz, a third harmonic which is 20% of the fundamental, a 5th harmonic which is 10% of the fundamental and at as phase angle of 1.2 radians lagging. 1. Write down an expression for the...

Homework Statement Measurements taken of a square-wave signal using a frequency-selective voltmeter (called a spectrum analyzer) show its spectrum to contain adjacent components (spectral lines) at 98kHz and 126kHz of amplitudes 63mV and 49mV, respectively. For this signal, what would direct...

Homework Statement p(t)={ -1 from -1/220 to -1/330 0 from -1/330 to -1/660 1 from -1/660 to 1/660 0 from 1/660 to 1/330; -1 from 1/330 to 1/220 } p(t) represents the period of the excess air pressure of a sound wave. Find the harmonics...

Homework Statement Prove that {Y_{L}^{M}\left ( 0,\varphi \right )=\left ( \frac{2L+1}{4\pi } \right )^{1/2}\delta _{M,0}Homework Equations Y_{L}^{M}\left ( \theta,\varphi \right )=\left ( \frac{(2L+1)(L-M)!}{4\pi(L+M)! } \right )^{1/2}P_{L}^{M}(cos\theta )e^{im\varphi } \int_{\varphi...

Homework Statement Evaluate the integral ∫∫dΩ V(Ω)Yml(Ω) for V(Ω) = +V0 for 0<θ<π/2 ; -V0 for π/2<θ<π Homework Equations I was hoping to apply the orthonormality properties of the spherical harmonics but this is a little more difficult since the integral breaks into two integrals over...

Hello PF, This is my first EVER thread in this website. Excuse me for my bad english. I'm a junior high student from Thailand. Yep, you heard it, Junior high. (Studying in a Math-Sci Program) Back to the topic. Can you give me some basic ideas on simple harmonics? I've just finished...

Homework Statement I'm trying to solve I_l = \int^{\pi}_{0} d \theta \sin (\theta) (\sin (\theta))^{2l} Homework Equations the book suggest: I_l = \int^{+1}_{-1} du (1 - u^2)^l The Attempt at a Solution I think it's something related to Legendre polynomials P_l (u) =...

Okay, so I'm working on using spherical harmonics to fit a model to some data. The thing is, everything can apparently be described as a "linear combination of spherical harmonics" but nobody is explaining in plain English what that means, at least to me! :D I see lots of double sum...

I'm having a hard time grasping the logical flow from orbital angular momentum to spherical harmonics. It feels like it's just sort of been sprung out of nowhere from both my lecture notes and the textbook. Can anyone help fill in the gaps that clearly must link them somehow? How did I get from...

I have a problem consisting in solving for potential in 2 dim polar coordinates where I am asked to use circular harmonics. Can I still use Legendre polynomials (since these are actually for spherical harmonics)? If not what are their analoguous in polar coordinates?

Hey guys I am trying to understand a code for a Fortran 77 subroutine which calculates spherical harmonics using the CERN library RASLGF for legendre functions. The code looks like this subroutine harmonics(max,theta,phi,Yr,Yi) implicit none integer max,k,nn,n,grens...

Harmonics is one of those things that few understand...especially Harmonics is one of those things that few understand...especially me. Does anyone have a real understanding on the subject as it pertains to electrcial engineering? At least introduce some basic things about it that even...

We have many harmonics in a string [PLAIN]http://img43.imageshack.us/img43/3452/dfshfghdfh.jpg Why when we play a guitar string with the finger it vibrate in n=1, where L = lambda/2 Even when we press the string in a given position (to make another note for example)...

Hi, I have the following question: An A.C. voltage, V comprises of a fundamental voltage of 100V rms at a frequency of 120Hz, a 3rd harmonic which is 20% of the fundamental, a 5th harmonic which is 10% of the fundamental and at a phase angle of 1.2 radians lagging. (1) Write down an...