Unit 5

Question 1

Wavepacket

Answer 1

A group of superposed waves which together form localized disturbances. A packet of waves encompassing a finite number of wave cycles
ex.) musician plays a note for a finite time, wave propagates out as a wave packet of finite length

Question 2

Disturbance

Answer 2

Change or deviation from a system’s equilibrium state, which when propagated through a medium, creates a wave

Question 3

Quantum Mechanics

Answer 3

the field of physics that explains how extremely small objects simultaneously have the characteristics of both particles (tiny pieces of matter) and waves (disturbance/variation that transfers energy)

Question 4

Wave function 𝚿

Answer 4

a function that describes the properties of a particle. Its square is proportional to the probability of finding the particle at a particular point in space. Maps out what the wave of an electron might look like in three dimensions. Describes the distribution of particles when the system has a specific energy value.

Question 5

Traveling wave

Answer 5

a wave that propagates through space (ex. light, x-rays, and gamma rays, which describe unbound electrons)

Question 6

Propagate

Answer 6

transmit or be transmitted in a particular direction or through a medium

Question 7

standing wave

Answer 7

a wave that vibrates in a fixed region (ex. guitar string with fixed ends, which describe bound electrons)

Question 8

Unbound electrons

Answer 8

electrons not bound to atoms, are described by traveling waves i.e. wavepackets, can have any wavelength and momentum

Question 9

Bound electrons

Answer 9

electrons held within an atom, may only have certain wavelengths (2L/n), are described by standing waves

Question 10

Condition/wavelength of a standing wave

Answer 10

2L/n
-L: distance between end points
-x: position in space between fixed points

Question 11

Classical standing waves

Answer 11

waves that are constrained to a region of space (“a box”)

Question 12

The fundamental harmonic/frequency

Answer 12

n=1, the standing wave with the fewest nodes

Question 13

harmonic

Answer 13

a wave or signal with a frequency that is a whole number multiple of the fundamental frequency, higher values of n correspond to higher harmonics, more nodes, shorter wavelengths, higher frequencies, and higher energy

Question 14

Node

Answer 14

a region of no vibration (0 amplitude) of a standing wave. The higher number of harmonic, n, the more numerous the nodes

Question 15

quantum number (n)

Answer 15

characterize the possible states of the system

Question 16

Schrodinger’s wave function

Answer 16

characterizes the wave associated with a particle at a position located by the coordinates x, y, z at time t

Question 17

Schrodinger’s equation

Answer 17

the fundamental equation of quantum mechanics that relates the wave function of one or more particles to their masses and potential energies

Question 18

quantum electrodynamics

Answer 18

a relativistic quantum theory that accounts for the interactions between matter and radiation (energy that travels as waves or particles)

Question 19

Stationary state

Answer 19

a standing wave that exists indefinitely, time independent. Confined to a space by a potential V(x)

Question 20

V(x)

Answer 20

potential energy function for the system of a particle or particles interacting with a set of constraints

Question 21

Probability (𝚿^2)

Answer 21

Probability density. the probability of finding a particle, proportional to the square of the amplitude of the electric field. For wave functions, 𝚿^2 is the probability that the particle will be found in a small volume centered at the point (x, y, z)

Question 22

Boundary conditions

Answer 22

the points at the fixed ends, forces a standing wave. restrictions that must be placed on the solutions to differential equations to reflect certain conditions known in advance about the system.

Question 23

discrete energy

Answer 23

concept that in certain systems like atoms, energy can only exist in specific, fixed values (only as packets of certain sizes)

Question 24

Particle in a box model

Answer 24

A particle confined by potential energy barriers to a certain region of space (“the box”). Since potential energy is infinite at boundaries, it is 0 inside box, and total energy will be positive at each point inside box

Question 25

Wave function for 1-D particle in a box

Answer 25

Ψ̅(x) = (√2/L)(sin(nπx/L))
(in sin equations, sin(nπ) will always be 0 at x=L)

Question 26

Energy (En) for particle described by wave function 𝚿n

Answer 26

En = (n²h²)/(8mL²)
KE=En

Question 27

Amount of nodes per wave function

Answer 27

n-1

Question 28

Max amplitude of wave function

Answer 28

+√2/L

Question 29

Probability density of PIB model

Answer 29

Ψ̅²(x) = (2/L)(sin²(nπx/L))

Question 30

quantum

Answer 30

-a discrete quantity of energy proportional in magnitude to the frequency of the radiation it represents
-describes many systems classical physics cannot