Spherical coordinates Definition and 337 Threads

In quantum mechanics the momentum operator is a constant multiplied by the partial derivative d/dx. In spherical coordinates it's turning into something like that: constant*(1/r)(d^2/dr^2)r can anyone explain please how this result is obtained?

Homework Statement Convert the point `(rho,theta,phi) = (6, (5pi)/4, pi/2)` to Cartesian coordinates. Give answers as positive values, either as expressions, or decimals to one decimal place. The Attempt at a Solution {x}=r*sintheta*cosphi {y}=r*sintheta*sinphi {z}=r*costheta So...

Homework Statement Given the gradient del = x-hat d/dx + y-hat d/dy + z-hat d/dz in rectangular coordinates, how would you write that in spherical coordinates. I can transform the derivatives into spherical coordinates. But then I need to express the rectangular basis vectors in terms of...

Hello - I'm supposed to derive the divergence formula for spherical coordinates by carrying out the surface integrals of the surface of the volume in the figure (the figure is a piece of a sphere similar to a box but with curves). The radial coord is r. The polar angle is \varphi and the...

Integrate the function f(x,y,z)=6*x+5*y over the solid given by the "slice" of an ice-cream cone in the first octant bounded by the planes x=0 and y=sqrt(43/5)*x and contained in a sphere centered at the origin with radius 13 and a cone opening upwards from the origin with top radius 12...

Homework Statement I have a vector A and B in spherical coordinates, and I need to find: part a) The vector component of B in the direction of A. part b) The vector component of B perpendicular to A Homework Equations dot product cross product The Attempt at a Solution...

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I need to derive the expression for the gradient operator in spherical coordinates. I know the following R =sqrt(x^2+y^2+z^2) theta, call it %, = arctan sqrt(x^2+y^2)/z phi, arctan (y/x) Using dT/dx= dT/dR*dr/dx+dT/d%*d%/dx+dT/dphi*dphi/dx, do partial derivates... dR/dx =...

I want to derive equation of continuity in spherical coordiantes based on shell balance,can anybody tell me where the hell this sin(theta) comes from? i don't want to transform from cartesian,

Hello everyone, this is an example out of the book, but I'm confused on how they got the spheircal cordinates. Here is the problem: Evaluate tripple integral over B (x^2+y^2+z^2) dV and use spherical coordinates. Well the answer is the following: In spherical coordinates B is represented by...

Hi guyz, I have a small question, In spherical coordinates if we define 2 vectors such as magnetization of a shell M(r,phi,theta) and the magnetic field H(r,phi,theta) As we know the cross product between them is written in the determinant: (Capital means unit vectors) det[(R,r...

If using spherical coordinates (r, theta, phi) , what is the meaning of the canonical momentum of theta, phi? What are their definitions and mathematical form? In solving the Hydrogen problem, one has not take into consideration P_theta and P_phi at all. Quantum River

I need to use spherical coordinates to try and find the volume of the region bounded by x2 + y2 + z2 = 2 which converts to p=Sqrt.(2) a sphere and z = x2 + y2, a parabloid which I converted to cot(phi)csc(phi)=p I hope the greek letters for these are comonly used...

Hey... Could someone help me out with deriving the LaPlacian in spherical coordinates? I tried using the chain rule but it just isn't working out well.. any sort of hint would be appriciated. :) \nabla^2 = \frac{1}{r^2} [ \frac{\partial}{\partial r} ( r^2 \frac{\partial}{\partial r} ) +...

Im new to this forum but not new to science and math at all. But i have a mathematical problems. I've been working with QM for a while and I am having problem with this specefic integral. This integral that is included in the word file is the integral I am having problems with. In my papers the...

Hi, I am having trouble starting off this question. Could someone help me start off? Thanks in advance... Use spherical coordinates to evaluate ∫∫∫н (x² + y²) dV, where H is the hemispherical region that lies above the x-y plane and below the sphere x² + y² + z² = 1.

Hi I am trying to calculate L^2 in spherical coordinates. L^2 is the square of L, the angular momentum operator. I know L in spherical coordinates. This L in spherical coordinates has only 2 components : one in the direction of the theta unit vector and one in the direction of the phi unit...

can anyone help me with this question: A sphere of unit radius is centered at the origin. points U,V & W on the surface of the sphere have vectors u,v & w. find the position vector of points P&Q on a diameter perp to the plane containing points U,V & W? can anyone help

I have no idea how to do this. I've tried a lot of things but I can never reduce it to solely cartesian coordinates. Is there any hard fast procedure to conversions like this? thanks.

Wondering if someone could help me get this answer. I don't get spherical coordinates at all. The volume of the region given in spherical coordinates by the inequalities 3 less than or equal to rho less than or equal to 5 0 less than or equal to phi less than or equal to pi/6 -pi/6 less...

What is equivalent to the unit k (vector in cartesian coords) in spherical coordinates? And why? z=rcos(t)

Hi, I am studying for finals and I'm having trouble calculating flux over sections of spheres. I can do it using the divergence theorem, but I need to know how to do it without divergence thm also. The problem is, when calculating a vector field such as F(x, y, z) = <z, y, x>, say over...

Hello. Here is the problem I am currently having difficulties with: "find the volume of the solid that lies inside the cone z^2 = 3x^2 + 3y^2 and between spheres x^2 + y^2 + z^2 = 1 and x^2 + y^2 + z^2 = 9" I know that this integral needs to be setup in spherical coordinates... Here is the...

Hi, I am having trouble with spherical coordinates. For example, how do you express the unit vectors x hat, y hat, z hat in terms of the spherical unit vectors r hat, theta hat, phi hat. I was able to go from spherical in terms of cartesian (with the help of mathworld.wolfram.com) but I can't...

Hi, I'm having trouble setting up an integral for the following problem. Q. Let D be the region inside the sphere x^2 + y^2 + z^2 = 4 in common with the region below the cone z = \frac{1}{{\sqrt 3 }}\sqrt {x^2 + y^2 }. Using spherical coordinates find the mass of D if the mass density...

how do you express angular velocity in spherical coordinates? like the Earth rotates with constant speed, so the direction of the angular velocity vector is out the north pole. if it was spherical coordinates , how do you specify that direction? i know that z = r cos theta so \hat{k} = r...

Hi, I was just reading up on some astrophysics and I saw the line element (general relativity stuff) written in spherical coordinates as: ds^2 = dr^2 + r^2(d\theta^2 + \sin\theta\d\phi) I don't get this. dr is the distance from origo to the given point, so why isn't ds^2 = dr^2 without...

Hi, Please can someone help me with this problem: find the triple integral over T( using spherical coordinate) T: 0<=x<=1 0<= y<=sqrt(1-x^2) sqrt(x^2+y^2)<= z <= sqrt(2-(X^2+y^2)) please help me just to find the boundaries of the integrals. I tried but I did not find the...

Just curious, why is \phi calculated as the angle between the +z axis and a position vector of a point of a function, as projected onto the yz plane? Why this convention? In polar & cylindrical, \theta is calculated from the +x axis to the +y axis (counterclockwise) for position vectors...

im having trouble determining the angles of phi in spherical coordinates when asked to convert a triple integral into spherical, and find the limits of the phi integral. can anybody point out any hints/tips/tricks how this may be done??Please...i have an exam tomorrow and I am tryn to prepare...

Hi, I need to find the volume of the solid that lies above the cone with equation (in spherical coordinates) \phi = \frac{\Pi}{3} and inside the torus with equation \rho = 4\sin\phi . I thought that the bounds are: 0\leq\rho\leq4\sin\phi, \frac{\Pi}{3}\leq\phi\leq\frac{\Pi}{2}, and...

i have a question concerning transforming triple integrals into spherical coordinates. the problem is, i do not know how to find the limits of phi. Can anyone help me? Thanks...

Here is the problem: Find the volume of the region enclosed by the spherical coordinate surface \rho = 2 \sin\theta, using spherical coodinates for the limits of the integral. Here is what I have: I don't know if this is right, but here it is...

How do I get the bounds for a function w/out drawing a graph?? Like, Volume of the solid bounded above by the sphere r^2+z^2=5 and below by the paraboloid r^2=4z. How would I get the bounds for these in cylindrical coordinate (r dz dr dtheta)? ***Mass of the solid inside the sphere p=b and...

I have a hemispherical surface of radius R with it's base centred on the origin. We are using the convention: r is the radius i.e. the magnitude of the position vector of a point: its distance from the origin. theta is the polar angle phi is the azimuthal angle I am asked to...

I'm trying to find the line element in spherical coordinates as well as a velocity element. I know that they are (ds)^2=(dr)^2+r^2(sin(theta))^2(dtheta)^2+r^2(dphi)^2 and sqrt[(dr/dt)^2+r^2(sin theta)^2(dtheta/dt)^2+r^2(dphi/dt)^2]. I know that this should be a quick and easy problem, but I...

Do you know of any freeware available for graphing (3D) spherical coordinates -- like Maple (only freeware)?