MIT 8.04

Question 1

If an electron goes through a box that sorts it based on color, and then white electrons sorted go through another color sorting box, what percentage of the electrons in that box are white?

Answer 1

100%

Question 2

Say an electron goes through a box that sorts if based on color. If the electrons found to be white are then sorted by hardness and the soft electrons in that group are put through another sorting box, what is the ratio of black and white electrons?

Answer 2

50/50

Question 3

Electrons are added to a hardness sorting box and hard electrons are sorted out the top and soft electrons are sorted out the side. The electrons from each side are then reflected against mirrors in the perpendicular direction until both sets of electrons meet again and are put through another hardness box. What is the ratio of hard to soft electrons?

Answer 3

50/50

Question 4

Hard electrons are added to a hardness sorting box and hard electrons are sorted out the top and soft electrons are sorted out the side. The electrons from each side are then reflected against mirrors in the perpendicular direction until both sets of electrons meet again and are put through a color sorting box. What is the ratio of black to white electrons?

Answer 4

50/50

Question 5

White electrons are added to a hardness sorting box and hard electrons are sorted out the top and soft electrons are sorted out the side. The electrons from each side are then reflected against mirrors in the perpendicular direction until both sets of electrons meet again and are put through a color sorting box. What is the ratio of black to white electrons?

Answer 5

100% white

Question 6

White electrons are added to a hardness sorting box and hard electrons are sorted out the top and soft electrons are sorted out the side. The hard electrons from are then reflected against a mirror in the perpendicular direction and the soft electrons are blocked by a barrier. The remaining electrons are put through a color sorting box. What percentage of the electrons make it to the color box and what is the ratio of black to white electrons?

Answer 6

Electron output is down by 50%, with a 50/50 color ratio

Question 7

What is superposition?

Answer 7

Superposition is a position between two states (ie black or white, hard or soft) where an object is not exclusively one state, nor both nor neither

Question 8

What happens to the initial voltage of a beam of light as the intensity changes?

Answer 8

V_0 is independent of I and linear in frequency 𝜈

Question 9

What two equations did Einstein derive from the photoelectric effect?

Answer 9

E = h𝜈 (where h is Plank’s constant and 𝜈 is frequency) and P = h/λ

Question 10

How does light behave like a wave?

Answer 10

According to the double slit experiment, light is a distributed object which is not localized and it can interfere with itself

Question 11

How does light behave like a particle?

Answer 11

According to the Hitachi double slit experiment, individual photons hit localized spots and they do not interfere with themselves

Question 12

If we shoot a single electron at a screen in a double slit experiment setup, what do we know about the path it takes?

Answer 12

The path it takes is in superposition between the two slits

Question 13

Does Bell’s inequality apply in quantum mechanics?

Answer 13

No

Question 14

The state of a quantum object is completely specified by what?

Answer 14

A wave function 𝚿(x), which is a complex function

Question 15

What equation determines the probability density that object state 𝚿(x) will be found at x?

Answer 15

P(x) = |𝚿(x)|^2

Question 16

What can be determined given two possible configurations of a quantum system?

Answer 16

Given two possible configurations of a quantum system corresponding to two wave functions, 𝚿_1(x) and 𝚿_2(x), the system can also be in a superposition of these (𝚿(x) = a𝚿_1(x) + b𝚿_2(x) where a and b are complex numbers)

Question 17

How can any f(x) be built by superposing enough plane-waves?

Answer 17

Fourier transforms

Question 18

Two particles, 1 and 2, are described by plane wave of the form exp[ikx]. Particle 1 has a smaller wavelength than particle 2. Which particle has the larger momentum?

Answer 18

Particle 1

Question 19

What is Noether’s Theorem?

Answer 19

To every symmetry is an associated conserved quantity

Question 20

What makes an operator linear?

Answer 20

A linear operator respects superposition

Question 21

What do we mean when we say that the Schrodinger equation is unitary?

Answer 21

It conserves probability

Question 22

What is a degenerate eigenfunction?

Answer 22

A degenerate eigenfunction is an eigenfunction of some operator from which we can take arbitrary linear combinations and get another degenerate eigenfunction

Question 23

What properties does a wave equation have to satisfy in an infinite square well in order to be valid?

Answer 23

It has to vanish at the walls (satisfy boundary conditions), be normalizable and continuous

Question 24

Compared to the infinite square with the same with a, the ground state energy of a finite square well is…

Answer 24

lower energy

Question 25

If f(x) and g(x) are wave functions and c is a constant, then (c.f|g) = ?

Answer 25

c*(f|g)