task:
(a) Check that it meets the vector potential
condition 
, where B is a constant magnetic
field.
(b) Let A be the vector potential given under (a). Show that he is
a member
occurring in the Hamilotonian for a particle in the EM field equal
to the expression for the interaction of the magnetic moment
μL
due to the orbital angular momentum with the magnetic field B
where q is the charge and a m is the mass of the particle.
Homework Answers
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task:
(a) Check that it meets the vector potential
condition , where B is a constant...
4. An atom with orbital angular momentum 1=1 is subject to a constant magnetic field B...
4. An atom with orbital angular momentum 1=1 is subject to a constant magnetic field B = B(sine cos o, sin sine, cos e), where B is a constant o, o give the direction for B The atom is described by the Hamiltonian. EM L.B Determine ifs energy Spectron
qm 09.3 3. An operator  is Hermitian if it satisfies the condition $ $(y) dx...
qm 09.3
3. An operator  is Hermitian if it satisfies the condition $ $(y) dx = (Ap) u dx, for any wavefunctions $(x) and y(x). (i) The time dependent Schrödinger equation is ih au = fu, at where the Hamiltonian operator is Hermitian. Show that the equation of mo- tion for the expectation value of any Hermitian operator  is given by d(A) IH, Â]), dt ħi i = where the operator  does not depend explicitly on time....
(1 point) A uniform magnetic field B has constant strength b teslas in the 2-direction [ie., B = (0,0, b) ] (a) Verify that A Bx r is a vector potential for B, where r (x,y,0) (b) Calculate the flux...
(1 point) A uniform magnetic field B has constant strength b teslas in the 2-direction [ie., B = (0,0, b) ] (a) Verify that A Bx r is a vector potential for B, where r (x,y,0) (b) Calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. FIGURE 17 A= (4,0,4), С=(0,3,0), В= (4,3,0), D (0,0, 4), F (4,0, 0) Flux(B)
(1 point) A uniform magnetic field B has constant strength b...
3. Consider the electromagnetic wave k=(0.2) where .A Draw the electric field E, magnetic field B and Poynting vector S at the points = (x, y, z) that fulfill: a) th when t-0. - e condition-k = 0 Sid...
3. Consider the electromagnetic wave k=(0.2) where .A Draw the electric field E, magnetic field B and Poynting vector S at the points = (x, y, z) that fulfill: a) th when t-0. - e condition-k = 0 Side view 3D view b) the condition F. k-2 when t-o. Side view 3D view 3.B Calculate the wavelength λ of the wave (6). Compare the magnitude of λ with the magnitude of k. 3.C Wave (6) is expressed in terms of...
(10 points) Un uniforme magnetic field B has constante strength b teslas in the z-direction [i.e., B-(0,0, b) ] (a) Verity that A-Bx r is a vector potential for B, where r (x,y,0) (b) Calculate the f...
(10 points) Un uniforme magnetic field B has constante strength b teslas in the z-direction [i.e., B-(0,0, b) ] (a) Verity that A-Bx r is a vector potential for B, where r (x,y,0) (b) Calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. FIGURE 17 A-(7, 0, 6) , B-(7, 3, 0) , C-(0, 3, 0) , D- (0,0,6), F-(7,0,0) Flux(B)
(10 points) Un uniforme magnetic field B has constante strength...
Problem 2 (10 pt.) A homogeneous sphere of mass m and radius b is rolling on...
Problem 2 (10 pt.) A homogeneous sphere of mass m and radius b is rolling on an inclined plane with inclination angle ? in the gravitational field g. Follow the steps below to find the velocity V of the center of mass of the sphere as a function of time if the sphere is initially at rest. Bold font represents vectors. There exists a reaction force R at the point of contact between the sphere and the plane. The equations...
4. An atom with orbital angular momentum 1=1 is subject to a constant magnetic field B = B(sine cos o, sin sine, cos e), where B is a constant o, o give the direction for B The atom is described by the Hamiltonian. EM L.B Determine ifs energy Spectron
qm 09.3
3. An operator  is Hermitian if it satisfies the condition $ $(y) dx = (Ap) u dx, for any wavefunctions $(x) and y(x). (i) The time dependent Schrödinger equation is ih au = fu, at where the Hamiltonian operator is Hermitian. Show that the equation of mo- tion for the expectation value of any Hermitian operator  is given by d(A) IH, Â]), dt ħi i = where the operator  does not depend explicitly on time....
(1 point) A uniform magnetic field B has constant strength b teslas in the 2-direction [ie., B = (0,0, b) ] (a) Verify that A Bx r is a vector potential for B, where r (x,y,0) (b) Calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. FIGURE 17 A= (4,0,4), С=(0,3,0), В= (4,3,0), D (0,0, 4), F (4,0, 0) Flux(B)
(1 point) A uniform magnetic field B has constant strength b...
3. Consider the electromagnetic wave k=(0.2) where .A Draw the electric field E, magnetic field B and Poynting vector S at the points = (x, y, z) that fulfill: a) th when t-0. - e condition-k = 0 Side view 3D view b) the condition F. k-2 when t-o. Side view 3D view 3.B Calculate the wavelength λ of the wave (6). Compare the magnitude of λ with the magnitude of k. 3.C Wave (6) is expressed in terms of...
(10 points) Un uniforme magnetic field B has constante strength b teslas in the z-direction [i.e., B-(0,0, b) ] (a) Verity that A-Bx r is a vector potential for B, where r (x,y,0) (b) Calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. FIGURE 17 A-(7, 0, 6) , B-(7, 3, 0) , C-(0, 3, 0) , D- (0,0,6), F-(7,0,0) Flux(B)
(10 points) Un uniforme magnetic field B has constante strength...
Problem 2 (10 pt.) A homogeneous sphere of mass m and radius b is rolling on an inclined plane with inclination angle ? in the gravitational field g. Follow the steps below to find the velocity V of the center of mass of the sphere as a function of time if the sphere is initially at rest. Bold font represents vectors. There exists a reaction force R at the point of contact between the sphere and the plane. The equations...
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