Quantum Mechanics Answers

An 800N elevator hangs by a steel cable for which allowable stress is 1.2 ×10^8 n/m².what is the minimum diameter required if the elevator accelerates upwards at 1.5 m/s²

If the functions Y1 and Y2 are solutions of the Schrödinger equation for a particle, then show that a1Y1 + a2Y2, where a1 and a2 are arbitrary constants, is also a solution of the same equation.

The current position of the harmonic oscillator is given by the relation 

x(t)=(0,4m)cos(πt/2).Time t is expressed in seconds. Find the maximum speed of the oscillator

The speed of a small truck increases from 36km/h to 72km/h During a three kilometer trip along a horizontal road.the mass of the truck is three thousand kilograms and the friction coefficient is 0.001.

1.) determine the work done and the average power developed by the trucks engine.

2.)same question if the truck travels uphill at an angle 10⁰

. Consider a voltage amplifier having a frequency response of the low-

pass STC type with a dc gain of 60 dB and a 3-dB frequency of 1000

Hz. Find the gain in dB at f = 10 Hz

If an amplifier working with ±5V DC power supplies, requires a 

minimum output voltage of 3V across a load resistance of 100 ohms, 

calculate the minimum current to be drawn from the power supply, if 

the efficiency of the amplifier is 35%.

If a particle in the harmonic oscillator potential is initially in a momentum eigenstate can the expectation value of an operator then be time dependent? I get that i doesen't happen if the particle is initially in an energy eigenstate but that it may happen if it is initially in a superposition of different energy eigenstates.

Find the wave function of two systems of identical, noninteracting particles: first consists of two bosons

and the second of two spin-1/2 fermions.

Two impedances Z1 and Z2 are connected in parallel. The first branch takes a leading

current of 16 A and has a resistance of 5 Ω, while the second branch takes a lagging

current at 0.8pf. The applied voltage is 100+j200 V and the total power is 5 kW. Find

branch impedances, total circuit impedance, branch currents and total circuit current.

Quantum mechanics is relevant, when the de Broglie wavelength of the particle is

greater than the distance between particles. The purpose of this problem is to determine

which systems will have to be treated quantum mechanically and which can be

described classically.

a) Show that the typical de Broglie wavelength of a particle in an ideal gas in

equilibrium is λ =h/√3mK B T

b) Solids: The lattice spacing in a typical solid is d = 0.3 nm. Find the temperature

below which the free electrons in a solid are quantum mechanical? (Hint: Refer the

a) part of the question and treat free electrons as a gas and the lattice spacing as the

typical distance between the electrons)

c) Gases: For what temperatures are the atoms in an ideal gas at pressure P quantum

mechanical? (Hint: Use the ideal gas law, to deduce the inter atomic distance)

Below what temperature, is Helium at atmospheric pressure quantum mechanical?

Below what temperature is Hydrogen atoms in outer space quantum mechanical?

(interatomic distance is 1 cm and temperature is 3 K)