physics

问题 I have a ladder operator â, which satisfies this commutator relation with its own adjoint: [â, â⁺] = 1 In sympy I have written this code: import sympy from sympy import * from sympy.physics.quantum import * a = Operator('a') ad = Dagger(a) ccr = Eq( Commutator(a, ad), 1 ) Now I need to expand and simplify an expression like this: (â⁺ + â)⁴ If I just use ((ad + a)**4).expand() , sympy doesn't use the commutator relation. How do I simplify the expression while using the canonical commutator

问题 I don't want to change ANYTHING other than the body that defines the shape of a SKPhysicsBody. How do I do this? I can't seem to find where I can change this. Or even commentary on how to change it. Yes, I know this has to be done carefully, so that it avoids all possible new collisions, overlaps, etc. But putting that aside, how do I change the body of an SKPhysicsBody? 回答1: You can manually create a custom shape for a physics body using CGMutablePath , then pass it into the SKPhysicsBody

问题 Let there be two balls, one of which is moving about in the Cartesian coordinate plane, while the other is stationary and immobile. At some point, the moving ball collides with the inert ball. Assuming the moving ball is traveling in a straight line, how can one derive the new angle that the moving ball will be propelled given the following information: The moving ball's center coordinates (X0, Y0), radius (R0), and angle of travel before impact (A0) The stationary ball's center coordinates

问题 I've been rehearsing Sprite Kit lately and I've come across a very strange problem. When zooming (changing the scale of) the parent node, bodies that are joined together by SKPhysicsJointPin separate from each other gradually and then joints break. Let me show you the images. This is for the normal state: Here's when zoomed in: And here's when zoomed out: If you ask how I join bodies: I join the brown sticks to the blue nodes on the center of the blue nodes. Any ideas what my problem is? EDIT

问题 I've been rehearsing Sprite Kit lately and I've come across a very strange problem. When zooming (changing the scale of) the parent node, bodies that are joined together by SKPhysicsJointPin separate from each other gradually and then joints break. Let me show you the images. This is for the normal state: Here's when zoomed in: And here's when zoomed out: If you ask how I join bodies: I join the brown sticks to the blue nodes on the center of the blue nodes. Any ideas what my problem is? EDIT

问题 So I have this body that is a circle collider and it has sometimes a big velocity the problem is that the tiled map of the boundaries is made of small tiles and at high velocity the body goes through it here is my config of all bodies: const config = { inertia: Infinity, // do not spin friction: 0, // X*100% stop on hit frictionAir: 0, // X*100% slow on move restitution: 0.5, // bounce X*100% on hit collisionFilter: this.level.getCollisionFilter(), // default collision filter isStatic } ...

问题 I am trying to have the ket symbol which is usually written in latex as \ket{\psi} . However, this doesn't work when written within the $$ ... $$ . This also doesn't work when written using IPython.display . 回答1: $ latex ** \documentclass{article}\usepackage{amsmath}\begin{document} ... chatter chatter ... * \show\ket > \ket=undefined. So your \ket macro is coming from some package or other which I don't know what it is. This doesn't explain why it doesn't work in $$ ... $$ -- you have to

问题 I am trying to have the ket symbol which is usually written in latex as \ket{\psi} . However, this doesn't work when written within the $$ ... $$ . This also doesn't work when written using IPython.display . 回答1: $ latex ** \documentclass{article}\usepackage{amsmath}\begin{document} ... chatter chatter ... * \show\ket > \ket=undefined. So your \ket macro is coming from some package or other which I don't know what it is. This doesn't explain why it doesn't work in $$ ... $$ -- you have to

问题 I am trying to have the ket symbol which is usually written in latex as \ket{\psi} . However, this doesn't work when written within the $$ ... $$ . This also doesn't work when written using IPython.display . 回答1: $ latex ** \documentclass{article}\usepackage{amsmath}\begin{document} ... chatter chatter ... * \show\ket > \ket=undefined. So your \ket macro is coming from some package or other which I don't know what it is. This doesn't explain why it doesn't work in $$ ... $$ -- you have to

问题 For my modelling and simulation class project, I want to simulate a solar system. I'm starting with just a star (sun) and a planet (earth), but I'm running into a few problems already. I've spent some time now just reviewing and learning about different formulas and way to simulate how the planet's orbits will be affected by the star and surrounding objects. I want to use velocity verlet and eventually look into the n-body problem. I'm having numerous issues with my velocity verlet function.