3d Definition and 1000 Threads

The matrix representation of a certain operator in a certain basis is $$\begin{bmatrix} 1 & 0 & 0 \\0 & 0 & -i \\ 0 & i & 0 \end{bmatrix} .$$ The eigenvalue problem leads to this equation $$0=det\begin{bmatrix} 1-\lambda & 0 & 0 \\0 & -\lambda & -i \\ 0 & i & -\lambda \end{bmatrix}...

1. Since N is large, ignore the kinetic energy term. ##[-\mu + V(r) + U|\Psi (r)|^2]\Psi (r) = 0## 2. Solve for the density ##|\Psi (r)|^2## ##|\Psi (r)|^2 = \frac{\mu - V(r)}{U}## 3. Integrate density times volume to get number of bosons ##\int|\Psi (r)|^2 d\tau = \int \frac{\mu -...

Summary:: I am trying to find the exact ground state energy of the hamiltonian.kindly help me with this

I'm sorry if the wording is a bit clunky, but this is not a common topic for me. Say you have some 3D object consisting of vertices and facets. There are many tools that can visualize this and they only show its projection on 2D, i.e. on your screen. I presume that you would filter the faces...

Many years ago I went to the cinema to watch Avatar in 3D, and was provided with polarising 3D glasses at the venue. I can't remember if it was my first 3D film that involved polarising projection technology, but it was certainly one of my first. In any case, the 3D effect worked and I got...

I spent the past week and a half making this 3D model using a program called Blender 3D, or the Fukushima Daiichi nuclear power plant control room.

A 3d printer that could print metal and other materials would revolutionize everything. The only problem is that metals have a really high melting point, so if you try to get a metal hot enough to bind to the other metals in its vicinity it would probably destroy the bonds of the neighboring...

Hi, 2 part question trying to get tetrahedron Finite Element shape functions working: 1) How do I properly setup the shape coefficient matrix and 2) How do I build the coefficient quantities in the shape functions properly? ANY tips or corrections may unblock me and would be of much value...

These are images of a 3D model I made of the legendary Edmund Fitzgerald, a great lakes bulk carrier ship, which famously sank in lake superior in 1975.

Made using Blender 3D, version 2.9, rendered in eevee. https://www.artstation.com/artwork/oAmVDw

Hello, I am clear on 1D and 2D Numpy arrays, how to create them and address them). 1D array: single list 2D array: list containing multiple lists as elements 3D array: list containing lists which contain lists as elements Array elements can be address using indices as a[], a[][], a[][][]...

Dear All, I'm a french professional photographer working on Still Life and Architecture. As a long time and personnal project I'm working on a 3D printed/Laser cut analog camera that will shoot 6x4.5 frames. In the end it will be some kind of rangefinder with integrated electronic light...

Currently I am working on an assignment about making an extruder screw for screw based 3D printer. I am confused that actually what kind of machines those manufactures out there using to manufacture this kind of extruder screws ?

Is the following realizable : We suppose two non visible lasers whose direction and phase could be changed very quickly. The energy of just one laser would correspond to no possible transition in the atomic spectra of the molecules present in the atmosphere of the room. However if both...

If we were to use three-dimensional spheres to represent sets, could a 3D Venn diagram be constructed that could not be drawn as a normal 2D Venn diagram without changing the relationships between the sets?

I've been struggling with the problem below for some time. It is not a homework. A simple bubble S is a spherical surface that expands with constant speed c. A vector bubble V also expands with the same constant speed c. There is a 3d vector associated with a V. If two S bubbles touch, they...

Just recently, I finally upgraded my 7+ year old computer. I was able to find a good deal on a HP Omen, with a Geforce RTX 2060 graphics card. So, not only was I able to upload the latest build of Blender, but I was able to go back and tweak some renders I had done with the old computer. For...

Summary:: Can anyone help me with this 3d Volumetric Strain and Volume Change. The is question is attached as a document below with the question and my attempt at the answer All questions and attempted answers are in the attached file below

I hope to explore mechanical engineering one day so I can answer these kinds of questions on my own, but until then, I appeal to anyone that knows how to do this to help me. I am building a core xy 3D Printer and I want to use a belt driven Z axis. I will have 3 or 4 stepper motors to drive...

Okay so I need to find 12 one dimensional first order equations that describe the position and velocity of both masses in 3 dimensions. The equations for the second body will be easy once I figure out how to do the first body, so I'll ignore that for now. For the first equation, I can rearrange...

This is a 3D model I made of the Mir space station.

Via web search found https://www.physicsforums.com/threads/what-dimension-does-space-time-curve-in.852103/ Read it and watched two videos mentioned: I understand we cannot perceive 5D ;-), so extrinsic visualization of maximum of 2D intrinsic curvature is possible. So time+1d space is all we...

Hi, so the four-dimensional generalization of $$\vec{B}=\mu\vec{H}$$ is $$F_{\lambda \mu}u_{\nu} + F_{\mu \nu}u_{\lambda} + F_{\nu \lambda}u_{\mu} = \mu (H_{\lambda \mu}u_{\nu} + H_{\mu \nu}u_{\lambda} + H_{\nu \lambda}u_{\mu})$$ From these four-tensors and four-vector I should be able to...

How did you find PF?: Google I am studying the mechanical/electrical nature that govern certain nano-fabricated crystalline structures. Can someone with experience please recommend a 3d Solid State Simulation software that will allow me perform the following: Allows individual 3D placement...

I was wondering if it's possible to plot a wave function that is a function of 3 coordinates, such as (x, y, z). The text my class uses calls this Quantum Mechanics in 3 dimensions, but wouldn't this technically by four dimensions?

Is the intersection of a 4D line segment and a 3D polyhedron in 4D a point in 4D, if they at all intersect? Intuitively, it looks like so. But I am not sure about it and how to prove it.

Suppose I have a three dimensional unit Vector A and two other unit vectors B and C. If B is rotated a certain amount in three dimensions to get vector C, how do I find what the new Vector D would be if I rotated Vector A the same direction by same amount?

Hi all, I'm working on programming a simple 2D method of characteristics program to design the nozzle wall contour for a supersonic rocket nozzle. I'm wondering roughly what sort of difference I should expect from a 2D vs 3D method of characteristics program and where I could find a good...

Assuming there are higher spatial dimensions are there things that exist in 3D that actually cannot exist in higher dimensions? Maybe even dimensions?

The boom is supported by a ball-and-socket joint at AA and a guy wire at BB Hey guys, I am stuck with this question in find the Tension in B and the moments around A. I have done plenty of 2d Tension questions but not a 3D one.

Hello, I am aware that the workflow of 3D printing involves the following steps: 1) Design the part using CAD and saving it as a .stl file. 2) Import the stl file into a slicing software to be converted to a G-code file 3) Load and run the G-code file on the 3D printer It is simple and safe to...

Hello, I understand that CAD models (stl files) suitable for 3D printing must be "watertight" and not leaky in the polygon mesh. By analogy, if we filled the model with water, the water would not leak...This concept of watertightness means that there are no unintentional holes between the...

I have this idea for LED eyes. Basically its an LED screen behind a half spherical shape. I want the user only to see what's on the display if they are looking directly at it. So for that I would need to polarize the half sphere. The half sphere can be made out of anything, the problem is how do...

So I have a cube in 3d space and this cube is made out of 8 coordinate points at each corner. Now I have a temperature reading at each point of these corner points. Inside the box I have another point, I want to be able to use the information from the 8 points surrounding the the one middle...

Hi PF! Each element of an ##n\times m## matrix is complex valued. In the following code, I call this "domain". There is also an ##n\times m## matrix that is real valued, below I call this "f". I'd like to plot a 3D image where the ##x-y## plane is the complex plain given by the coordinates...

I'm having trouble finding the angle and displacement

This is the code line that i used to generate the following graphs ParametricPlot3D[{{1 + Cos[t], Sin[t], 2*Sin[t/2]}, {2 *Cos[t]*Sin[\[Phi]], 2*Sin[t]*Sin[\[Phi]], 2*Cos[\[Phi]]}}, {t, 0, 2 \[Pi]}, {\[Phi], 0, \[Pi]/2}, PlotStyle -> {Directive[Green, Thickness[0.025]], Yellow}...

What percentage of the universe’s A) total mass —including dark matter— and B) radiation energy is estimated to reside in: Inter-galactic space covering i) inter-galactic medium and ii) distinct inter-galactic astronomical objects; and Galaxies covering iii) inter-stellar gas clouds, iv) stars...

Plugging in the supposed ##G## into the delta function equation ##\nabla^2 G = -\frac{1}{4 \pi} \frac{1}{r^2} \frac{\partial}{\partial r} \left(\frac{r^2 \left(ikr e^{ikr} - e^{ikr} \right)}{r^2} \right)## ##= -\frac{1}{4 \pi} \frac{1}{r^2} \left[ike^{ikr} - rk^2 e^{ikr} - ike^{ikr} \right]##...

Hi all, I'm finding it difficult to start this line integral problem. I have watched a lot of videos regarding line integrals but none have 3 line segments in 3D. If someone can please point me in the right direction, it would help a lot. I've put down the following in my workings: C1...

I would like to solve a system of systems of equations Ax=b where A is an n x m x p tensor (3D) matrix, x is a vector (n x 1), and b is a matrix (n x p). I haven't been able to find a clear walk-through of inverting a tensor like how one would invert a regular matrix to solve a system of linear...

All in the summary, can't copy paste on phone :(

Given Theta1(angle of incidence) and alpha1(azimuth angle). how do we obtain the second reflection angle theta3 and alpha3? Assuming the surface to be a mirror reflection(theta1 = theta2). Need an equation when varied the incident angles we would obtain the second reflection angles or a method...

Let ## E=\left\{ (x,y,z) \in R^3 : 1 \leq x^2+y^2+z^2 \leq 4, 3x^2+3y^2-z^2\leq 0, z\geq0 \right\} ## - Represent the region E in 3-dimensions -represent the section of e in (x,z) plane -compute ## \int \frac {y^2} {x^2+y^2} \,dx \,dy \,dz## the domain is a sphere of radius 2 with an inner...

##z^2\leq x^2+y^2, z\geq x^2+y^2## I know the shapes of those inequalities, but the question is: How do i find if the point are external the shape or internal?

Hi I have noticed that while I have the grasp of the theoretical underpinnings of linear algebra, I need work on applying it to geometric problems (think computer vision and rigid body motion). So, I am looking for a book that allows me to practice 3D geometry problems. Is there any obvious...

I am uncertain if this belongs in the differential geometry thread because I don't know what area of mathematics my question belongs into begin with, but of the math threads on physics forums, this one seems like the most likely to be relevant. I recently watched a video by PBS infinite series...

How did you find PF?: Google Hi, I'm looking for advice on how to simulate a golf ball rolling on a green. The green will have been scanned using a 3d scanner by an Engineering Surveyor. I'm trying to model putting a golf ball from any position on the green, looking for a path line to the...