Quantum Mechanics Answers

1. Two pucks on a horizontal air table of the same mass (m1 = m2 = 6.0 g) have attracting

magnets. They are initially positioned very far from each other so that no attraction occurs.

The two were given a push and collide. The pucks end up moving at 1.40 m/s, 32° above the

–x–axis after the collision as shown. Initially, the first puck slides with a velocity 1.11 m/s due

west.

(a) What is the initial velocity (magnitude and direction) of the second puck?

(b) What is the change in kinetic energy of the system of two pucks as a result of the

collision?

Convert the following frequencies to wavelengths (please present the final answer in the most appropriate units to present the quantities in a succinct manner):

a. 10.37 Hz

b. 400.1 MHz

c. 1.91 GHz

d. 79 GHz

e. 167 MHz 

Solve the Schrödinger equation for the following potential:

V(x) = ∞ x<0
     = Vo 0<x<a
     = 0  x>a

Here Vo is positive and solutions are needed for energies E > 0. Evaluate all undetermined coefficients in terms of a single common coefficient, but do not attempt to normalize the wave function. Assume particles are incident from x = -∞.

Solve the Schrödinger equation for the following potential: V(x) = 0 x < 0 - V. 0 <x < a = 0 x > a Here Vo is positive and solutions are needed for energies E > 0. Evaluate all undetermined coefficients in terms of a single common coefficient, but do not attempt to normalize the wave function. Assume particles are incident from x = -infinity.

1. Assuming that an oscilloscope displays a V_max of 5.22V and V_min of 1.33V. Calculate the percentage of modulation. (5 points)
2. Three (3) AM broadcast stations are spaced at 18 kHz, beginning at 73 kHz. Each station is allowed to transmit modulating up to 6 kHz. Compute for the upper and lower sidebands of each station and plot it in the frequency domain. (15 points)
3. Given a V_max of 7.45V and a modulation index of 0.691, calculate for V_min. (5 points)
4. A station is given a carrier frequency of 88 kHz. Having a modulating frequency of 12 kHz, compute for the upper and lower sidebands of the station. (5 points)

1. Assuming that an oscilloscope displays a V_max of 5.22V and V_min of 1.33V. Calculate the percentage of modulation. (5 points)
2. Three (3) AM broadcast stations are spaced at 18 kHz, beginning at 73 kHz. Each station is allowed to transmit modulating up to 6 kHz. Compute for the upper and lower sidebands of each station and plot it in the frequency domain. (15 points)
3. Given a V_max of 7.45V and a modulation index of 0.691, calculate for V_min. (5 points)
4. A station is given a carrier frequency of 88 kHz. Having a modulating frequency of 12 kHz, compute for the upper and lower sidebands of the station. (5 points)

 What is the range of the shuttlecock launched with an initial speed of 6.3797 m/s at a 58.3699-degree angle with respect to the horizontal from a height of 1.8914 m in a planet where the downward gravitational acceleration has a magnitude of 11.8201 m/s²?

Normalization wave function if we know wave function a particle confined motion in a two dimension box with ling a and width b is psi*n_{x}, my * (x, y) = 2/(sqrt(ab)) * sin((n_{x}*pi)/a * x) * sin((n_{y}*pi)/b * y)

show that linear combination of e^ikx and e^-ikx is a eigen function of operator d²/dx²

show that [A,[B,C]]+[B,[C,A]+[C,[A,B]]=0