Quantum Mechanics Answers

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.

a)using the web function si1(x) for the harmonic oscillator (see table 5.3) calculate that <x^2> ; b) now find <p^2x >square x using the same wave function as in part (a); c)it can be shown that <x> = <px> = 0 and that the variance (square of the standard deviation) of any property is given by the expression (sigma)^2 =<a^2> - < a>^2. find (sigma)x(sigma)px using the solution in parts (a) and (b). d) re-evaluate (sigma)x(sigma)px using the ground state wave function (is)0 for the harmonic oscillator and father compare to the results given in pb 5-20 for (sigma)2x. rationalize whether your answer should depend on the state of the system (e) how to use answer compare to that of equation 4.45?

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)

Show that xp-px=ih for the ground state wave function of the quantum harmonic oscillator.

 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

√3𝑚𝐾𝐵𝑇

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/√3𝑚𝐾𝐵𝑇

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)

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

√3𝑚÷𝐾𝐵𝑇

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)

Is Helium at atmospheric pressure quantum mechanical? What about Hydrogen atoms in outer space (interatomic distance is 1 cm and temperature is 3 K)?