Calculate the commutator 2m between the kinetic energy and the position operators for a particle moving in one dimension. Please notice that in the answers (hbar) is h/2T. Oa. (hbar)? m² Ob. (hbar) OC. d. (hbar)? d m dx е. 2m
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- A.) i. Define the plane polar unit vectors ŕ and 0 and show that they are orthonormal. Determine dr dê and de de ii. Hence show that for the vector r(t) = r(t)ŕ dr · = rî +rðê, d²r and = - dt dt² († − rė²)ŕ + (2ŕė +rë)ê . iii. If a mass m moves in the plane along r(t) = a and (t) = 5t determine the shape of the motion and find its period. B) Show that the motion of an object under the universal gravitational force μη Fg is governed by the radial and angular equations of motion and μ = 0, 2r0+ rö = 0. Setting r(t) =R for some constant R, solve these equations of motion and determine the period of the motion. C) Consider the following non-linear differential equation *+5= x +4. Find the stationary solutions. Expand around each of the stationary so- lutions that you have found, in order to determine if they correspond to stable or unstable equilibria. D) Show that 1 5 E = 2 - 4x is a conserved quantity. Hence draw the phase-space diagram and de- termine for which values of E oscilations…Is my work good for 19 b)? I am not sure if it makes sense to do it this way please let me know :) the answer should be around 1.1 kNCLO 4 If the plane x+y+z-1=0 cuts the x-axis, y-axis, and z-axis at A, B, and C respectively. Find the perpendicular distance to the point P(2,6,9). В а. 9.24 b. 8.66 С. 9.81 d. None of the choices О е. 5.33 f. 5.67 N.
- Needs Complete solution with 100 % accuracy. Otherwise skip if u can't give answer both of them. Thank you.he veclor equal to -4? 4/Youtaravel northeast Ci.e 45) at 2.0mls for 10s, Then travel Southeast Ci.e, at -450) at tHe sane speed vel for 20s. What 1 Your final poSítion relative to 5) lalso called thedot He tao vertors F=2i+8; and What is the scalar product (t)^pid OF. ー2ペ+399 6 What is te smailange vectors A-3i+4 and B= -59+123? betweenthetus7. The Lagrangian of a particle of moving in dimension is given by: mass one m x - b x Where b is a positive constant. The coordinate of the particle x (t) at a time t is given by: b А. t? + C, t + C2 В. С, t + Cz bt bt C. C, Cos () + C2 Sin () D. C, Cosh () + Sinh () т m bt bt m т For your solution in question seven, show how you got it. All steps must be clearly shown and justified
- If [x, p]=in and π = _—_p²+ -—-k x², , evaluate the commutator [.]. 2m 00 O O P m iħ 2m -P ħ iħ ħ m 2m iħ m 2m -P -P -P iħ mQ.) Solve a ,b and cI have written down a y(x,t) for the given values, but I think that I am not supposed to solve for the problem and then sketch. Am I supposed to solve the y(x,t) for the problem? Before I sketch? The problem is #7.1