calculate the angles which the angular momentum vector forms with the z-axis in some 3 states of a particle on a sphere described by spherical harmonics Y2,2, Y2,-1, Y2-0
Y2,2 = (15/32)1/2 sin2 e-2i
Y2,-1 = (15/8)1/2 cos sin ei
Y2,0 = (5/16)1/2 (3cos2 - 1)
calculate the angles which the angular momentum vector forms with the z-axis in some 3 states...
Problem 1. Determine the angular momentum, the z-component of the angular momentum, and the energy of the rigid rotor in states defined by the following spherical harmonics (the moment of inertia is "1"): a) Yoo b) 722 c) V2.2 d) Y105
Tutorial: Angular Momentum and Torque III. Angular Momentum The angular momentum of a point particle is defined by: L = ixp. Here, is a vector that points from the point of rotation (or point around which the angular momentum is calculated) to the location of the particle and p = mb is the linear momentum of the particle. A Your little brother Joey is playing with his toy airplane. The airplane is tied to a string and its motor makes...
(a) Calculate the angular momentum of Earth that arises from its spinning motion on its axis, treating Earth as a uniform solid sphere. J · s (b) Calculate the angular momentum of Earth that arises from its orbital motion about the Sun, treating Earth as a point particle. J · s
(a) Calculate the angular momentum of Earth that arises from its spinning motion on its axis, treating Earth as a uniform solid sphere. J ·s (b) Calculate the angular momentum of Earth that arises from its orbital motion about the Sun, treating Earth as a point particle. J ·s
4. Draw the space quantization diagram of angular momentum for I 3. a. What is the orbital angular momentum vector, |4, in terms of h b. what are the angles with respect to the z axis for the m,-1, m.-2, and mi-3 cases?
Calculate the angular momentum for a rotating disk, sphere, and rod. (a) A uniform disk of mass 16 kg, thickness 0.5 m, and radius 0.9 m is located at the origin, oriented with its axis along the y axis. It rotates clockwise around its axis when viewed from above (that is, you stand at a point on the +y axis and look toward the origin at the disk). The disk makes one complete rotation every 0.7 s. What is the...
The angular momentum vector of a precessing gyroscope sweeps out a cone as shown in the figure below. The angular speed of the tip of the angular momentum vector, called its precessional frequency, is given by w, = t/L, where t is the magnitude of the torque on the gyroscope and L is the magnitude of its angular momentum. In the motion called precession of the equinoxes, the Earth's axis of rotation precesses about the perpendicular to its orbital plane...
3 Angular Momentum and Spherical Harmonics For a quantum mechanical system that is able to rotate in 3D, one can always define a set of angular momentum operators J. Jy, J., often collectively written as a vector J. They must satisfy the commutation relations (, ] = ihſ, , Îu] = ihſ, J., ſu] = ihỈy. (1) In a more condensed notation, we may write [1,1]] = Žiheikh, i, j= 1,2,3 k=1 Here we've used the Levi-Civita symbol, defined as...
3. (a) Draw a vector model figure illustrating the orbital angular momentum L and orbital magnetic dipole moment μ vectors for a typical atomic state, their z- components, and their Larmor precession in a uniform magnetic field B for an electron in the p-state of hydrogen. orbital magnetic dipole moment vectors, their sum the total magnetic dipole mo- b) Draw vector model fgures indicating the total angular momentum posibilities and (c) For one of the above states, draw a vector...
322 CHAPTER 5. ANGULAR MOMENTUM Problem 5.12 Consider a particle whose wave function is 1 222-x2-y2 4 A 3 xz (x, y, z) = 2 2 Calculate L2 (x, y, z) and L-y(x, y, z). Find the total angular momentum of this particle. (b) Calculate L+ y (x, y, z) and (Y L+ W). (c)If a measurement of the z-component of the orbital angular momentum is carried out, find the probabilities corresponding to finding the results 0, h, and -h....