Consider the case of a 3-dimensional particle-in-a-box. Given: 4 = 3πχ sin sin () sin пу (2πz) 1.5 What is the size of the box along the x-dimension? O 2 O 3 O 5 none are correct
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- What is y(x) given that d²y dx² +4e-2x = 0 where you have the boundary conditions: dy dx y = yo (a constant) at You have to integrate twice as this is a second order differential equation so you need two boundary conditions to get the complete solution. (Most people are better at differentiating then integrating so check your answer by differentiating it!) = q (a constant) at x = 0 x = 0Consider the following measurements of a mass and speed for an object using the formula determine the momentum uncertainty of the object. Express answer in g•m/s The velocity of a proton in an accelerator is known to an accuracy of 0.250% of the speed of light. What is the smallest possible uncertainty in its position in meters?
- If | jm > is an eigenstate of 1², then its eigenvalue is j(j+1)ħ², Z True FalseSuppose Fuzzy, a quantum-mechanical duck, lives in a world in which h = 2 J s. Fuzzy has a mass of 1.90 kg and is initially known to be within a pond 1.00 m wide. (a) What is the minimum uncertainty in the duck's speed? m/s (b) Assuming this uncertainty in speed to prevail for 4.90 s, determine the uncertainty in Fuzzy's position after this time. mThis problem is designed to give you practice using the Dirac delta function. Eval- uate the following integrals. Show your reasoning.