Separation Definition and 448 Threads

While separating variables in the Schrodinger Equation for hydrogen atom, why are we taking separation constant to be l(l+1) instead of just l^2 or -l^2, is it just to make the angular equation in the form of Associated Legendre Equation or is there a deeper meaning to it?

I'm would like to learn of the practicality of separating HHO gas released from a photovoltaic charged lead-acid battery bank for hydrogen storage, perhaps by exploiting the substantial difference in density of the two elemental gases. It occurred to me that were the gas emitted from batteries...

Homework Statement State a change to the separation of the fringe when a sheet of glass is placed in front of the bottom slit (this is a Double Slit Experiment). The light being passed is monochromatic red light. Homework Equations x = (landa)D / a The Attempt at a Solution After looking...

Consider a ball flying through the air. When there is turbulence, and the flow separates, say on a SMOOTH ball, then in the rear, there is circulation in the wide wake. There is pressure on the front, but no pressure on the rear due to the fact that the fluid is "busy" circulating around. So...

Could someone please go here... https://en.wikipedia.org/wiki/Flow_separation And explain to me the difference between Flow and Boundary Separation discussed in the opening. Because this explanation makes no sense to me. I have the problem. I just don't understand the difference.

Hi ! I need help on the following problem : I've got a liquid in a pipe that splits into 2 in a "T-junction" (see drawing below) : I want to know if the liquid will split equitably (50% to the left and 50% to the right) or not. Length after the elbow = 3m Inner Diameter 0,27 m Flow volume...

Does the Cluster Decomposition Principle explain the spacelike non classical correlations in EPR experiments without action at a distance ? With CDP defined : S α1α2β1β2 = S α1β1Sα2β2 Does this definition equate to the locality assumption : P(A,B|a,b,λ) = P (A|a,λ)P(B|b,λ) If so then does...

Homework Statement For accurate measurement of the fringe separation, a small as possible slit separation should be used. Homework Equations s=λD/d The Attempt at a Solution Why is this statement correct ?

Morning Mates, I have a question based in a statement take from Berkeley Physics Course, Vol.1 - Mechanics, pg. 102-103, where it reads, "Suspended molecules whose density (mass/volume) is different from that of the surrounding liquid will experience in the ultracentrifuge cell a strong force...

Homework Statement How do I know what value of m to use when using the equation? Here we had to use m = 1 to find the answer. Please refer to part 3 for the problem statement. Homework Equations Please refer to part 3 for the relevant equations. The Attempt at a Solution [/B]

Hi, I know it’s posible to add a filler to chewed gum to recycle and reuse this gum, but I’ve been thinking about the polyvinyl acetate separation from it to get products from it, do you know how could I? Thanks.

Hi PF, I'm trying to derive the Prandlt condition (not sure if it is Prandlt's work tough) for a fluid to separate from a surface in the boundary layer. The equation should be: ##\frac {\partial^2 v_x} {\partial y^2} = 0## which is quite "intuitive" to me. To derive it let's start from the...

Homework Statement Could someone explain how the property, $$\nabla (\frac{1}{R}) = -\frac{\hat{R}}{R^2}$$ where ##R## is the separation distance ##|\vec{r} - \vec{r'}|##, comes about? What does the expression ##\nabla (\frac{1}{R}) ## even mean? Homework EquationsThe Attempt at a Solution...

Homework Statement A parallel-plate capacitor has a plate area of 18.5 cm2 and a capacitance of 4.8 pF What is the plate separation? The value of the permittivity of a vacuum is 8.8542 x 10-12 C2/N⋅m2 Homework Equations C = κε0 (A/d) The Attempt at a Solution 4.8x10-12 =...

<Moderator's note: Moved from a technical forum and thus no template.> Hi all, hope you all had a great Christmas, I had a difficulty with theses two problems, 1. Show that y=1/x + x/2 is a solution of the differential equation, dy/dx=1-y/x, where y=1.5 and x=2 2. Solve the differential...

What are the methods for quantifying the amount of colloidal particles in sol mixtures?

I understand that colloids (at least those less than 0.7 um in diameter) are not filterable using conventional filters. But are there other physical separation methods that can separate them from solution, apart from using membranes? Centrifugation perhaps? I just want some confirmation. Thank you!

Within a cylinder with length ##\tau \in [0,2\pi]##, radius ##\rho \in [0,1]## and angular range ##\phi \in [0,2\pi]##, we have the following equation for the dynamics of a variable ##K##: $$\left( - \frac{1}{\cosh^{2} \rho}\frac{\partial^{2}}{\partial\tau^{2}} + (\tanh\rho +...

Homework Statement Homework Equations If i solve the wave equation using separation of variable and laplace tranform. Will i get the same answer ? The Attempt at a Solution

Good day all! I've got a granular mixture of PLA, ABS, HIPS, and PETG with a particle size of about a quarter inch, and I'm trying to isolate each polymer from the mix. PLA and PETG have densities of about 1.27g/ml, and ABS and HIPS have densities of around 1.06g/ml. I think a weighted solution...

Homework Statement Boundary conditions are i) V=0 when y=0 ii) V=0 when y=a iii) V=V0(y) when x=0 iv) V=0 when x app infinity. I understand and follow this problem (separating vars and eliminated constants) until the potential is found to be V(x,y) = Ce^(-kx)*sin(ky) Condition ii...

Hello, I haven't found any program that can be used to perform separation of variables on difficult PDEs. Is there such a method somewhere?

Hi. I was wondering if it is possible to apply separation of variables for a function of space and time obeying a non homogeneous differential equation. In particular, the heat equation: ##\displaystyle \frac{\partial \Phi(\mathbf{r},t)}{\partial t}-\nabla \cdot \left [ \kappa(\mathbf{r})...

I've solving some separation of variables exercises, and I have a doubt when it comes to the Laplacian $$ u_{xx} +u_{yy} =0 $$ I usually have a rectangle as boundary conditions, so I use the principe of superposition and arrive to $$ \dfrac{X''(x)}{X(x)} = - \dfrac{Y''(y)}{Y(y)} = - \lambda $$...

Hello! (Wave) I want to check if the method of separation of variables can be used for the replacement of the following given partial differential equations from a pair of ordinary differential equations. If so, I want to find the equations.- $[p(x) u_x]_x-r(x) u_{tt}=0$ - $u_{xx}+(x+y)...

Homework Statement two charges with the same charge q and mass m are moving with the same acceleration at each instant. calculate the separation between them. Homework EquationsThe Attempt at a Solution F=kqq/r^2 so, F= k q^2/r^2 r^2=kq^2/F let the acceleration be a, then F=ma. r= q√k/F...

I've added a graph of coincidence events vs. detector angular separation. This is for a electron-positron annihilation (gamma-gamma coincidence) experiment. Why does the plot have a finite width and not look like a delta function? I'm assuming this is because the experimental conditions are...

Hi, hope this is in the right place apologies if not While thinking about relativistic effects I had the fascinating thought about whether when two objects that are separated by space, they could both be in each other's past at the same time But if one is in one's past the other is in the...

I am investigating the nucleation on solid surface during liquid-liquid phase separation, I know the free energy change is and I don't know if it is correct to get Can someone calculate it to have a check?

Homework Statement In this lab we are going to be given a mixture containing sodium chloride [NaCl], silicon dioxide [SiO2], Iron filings [Fe], and calcium carbonate [CaCO3] The goal of the lab is to use separation and measurement techniques to determine the percent by mass of each specie in...

Homework Statement A double-spit experiment is performed with light of wavelength 600 nm. A wide viewing screen is 2m behind the grating. What is the distance between the two m=2 bright fringes on the screen? The slit separation given is 0.1 mm. Homework Equations Given the wavelength and...

Homework Statement As always, I wish I were allowed to upload a drawing ;) This is not a problem, this is a derivation of sorts, so I don't have any numbers. I have 3 points. one at the origin, a point charge q and a test charge Q I have a vector from the origin to the point charge q with a...

It seems that, in general, mathematicians prefer the (-,+,+,+) signature for the Minkowski spacetime metric while most physicists prefer the (+,-,-,-) signature. Is there any evidence that Nature actually prefers one over the other? As usual, thanks in advance.

hello there Im trying to do a derivation of tsiolkovsky's rocket equation, but i got stuck at the step when i have to use separation of variables (marked with red in the pic), i used maple to solve it, so i could get on with it, but i want to understand what is happening to solve this, so can...

I am reading D. J. H. Garling: "A Course in Mathematical Analysis: Volume I Foundations and Elementary Real Analysis ... ...At present I am focused on Chapter 1: The Axioms of Set Theory and need some help with Theorem 1.2.2 and its relationship to the Separation Axiom ... ... The...

I am reading D. J. H. Garling: "A Course in Mathematical Analysis: Volume I Foundations and Elementary Real Analysis" ... ... At present I am focused on Chapter 1: The Axioms of Set Theory and need some help with Theorem 1.2.2 and its relationship to the Separation Axiom ... ... The...

I was overlooking page 47 of "The Physics of the Manhattan Project" 2.2 Critical Mass: Diffusion Theory, and author Bruce Cameron Reed reported that: Can anyone explain how Bruce Cameron Reed got from (2.18) to (2.19) I tried plugging ## N(r,t) = N(r) N(t) ## into (2.18) to get (2.19), but it...

I don't get what is vacuum distillation anyone can help me with this

Do all airfoils(infinite wing) have a flow separation at a finite or zero AOA? I wonder if there exists such an airfoil that despite the presence of adverse pressure gradients, exhibits no flow separation phenomena, perhaps turbulent intensity could be high enough to sustain enough speed near...

hi, i want to know that how many techniques are being used for charge separation? and which one is more effective for solar cell? can you give some idea about it that which one is better and how to make better power conversion efficiency. after going thoroughly through literature review i am...

Homework Statement A system consists of a 5.0-kg cart and a 1.4-kg cart attached to each other by a compressed spring. Initially, the system is at rest on a low-friction track. When the spring is released, an explosive separation occurs at the expense of the internal energy of the compressed...

Hi, I wonder why wronskian must be constant. I know that p(x)W[u1(x),u2(x)]=constant, according to the Abel's theorem, but wouldnt there a special case that W[u1(x),u2(x)]=c/p(x). Then for this special case, W[u1(x),u2(x)]=/=c and satisfies Abel's theorem. Is it ok to ignore this special case?

When compared to laminar flows, the fluid "sticks" with the solid surface longer in case of turbulent flows. For example, the angle of separation for flow over a circular cylinder is 80 degrees for laminar flows, and 140 degrees for turbulent flows. What is the reason?

I have trouble understanding how a connection one-form can separate and tangent space##{T_u}P## of a principal bundle uniquely into horizontal and vertical spaces ##{H_u}P \oplus {V_u}P## since from the literature I am learning (mainly Nakahara' book), the connection one-form is a...

Homework Statement The distance between the 1st bright fringe and the 21st bright fringe in a Young's double-slit arrangement was found to be 2.7 mm. The slit separation was 1.0 mm and the distance from the slits to the plane of the fringes was 25 cm. What was the wavelength of the light...

Homework Statement Homework Equations There are no equations here, only theoretical knowledge The Attempt at a Solution Hi, My approach was this: I know that with the positive charge on the sphere being lowered into the cup I will have the inner area of the cup have a negative charge and...

Hi all , just curious if someone knows of any issues of Separation of Points in Ordinal 3-valued Logistic Regression. I think I have an idea of why there are issues with separation in binary Logistic -- the need for the S-curve to go to 0 quickly makes the Bo term go to infinity. Are there...

<< Mentor Note -- thread moved from the technical math forums >> I am getting stuck on this partial differential equation. Ut = Uxx - U + x ; 0<x<1 U(0,t) = 0 U(1,t) = 1 U(x,0) = 0 Here is my work so far : U = e-tw + x gives the new eq wt=wxx to get rid of boundary conditions : w=x+W Wt=Wxx...

I'm self-teaching through Tenenbaum & Pollard's "Ordinary Differential Equations", and for some reason I'm completely stuck on one of the problems, Ch.2, lesson 6, problem #6: Find a 1-parameter family of solutions for [...] the differential equation: 6) yx2dy-y3dx = 2x2dy. I didn't have...

Homework Statement A double slit apparatus is held 1.2 m from a screen. (a) When red light (λ = 600 nm) is sent through the double slit, the interference pattern on the screen shows a distance of 12.5 cm between the first and tenth dark fringes. What is the separation of the slits? (b) What...