Wavefunctions

Question 1

Born interpetation

Answer 1

The intensity of a quantum wave at a given point in space is proportional to the probability of finding the particle at that point by measurement.

Question 2

The intensity of a quantum wave at a given point in space is proportional to the probability of finding the particle at that point by measurement.

Answer 2

Born interpetation

Question 3

finding the probability that a particle will be in a certain area

Answer 3

integrate the squared wave equation over the are in questin

Question 4

integrate the squared wave equation over the are in questin

Answer 4

finding the probability that a particle will be in a certain area

Question 5

normalizing a wave function

Answer 5

a wave function, when the probability form infinity to negative infinity is found, can’t have a result higher than 1. If the result isn’t one then solve for a N^2 that will make it equal to 1

Question 6

a wave function, when the probability form infinity to negative infinity is found, can’t have a result higher than 1. If the result isn’t one then solve for a N^2 that will make it equal to 1

Answer 6

normalizing a wave function

Question 7

requirments for born interpetaion

Answer 7

no jumping to infinity, no more than one value per space, and both the equation and it’s derivative must be continuous.

Question 8

no jumping to infinity, no more than one value per space, and both the equation and it’s derivative must be continuous.

Answer 8

requirments for born interpetaion

Question 9

wave packet

Answer 9

a representation of the area where a quantum partical could be. Marking one spot makes it look like a clasical particle.

Question 10

a representation of the area where a quantum partical could be. Marking one spot makes it look like a clasical particle.

Answer 10

wave packet

Question 11

equation for a particle in a box

Answer 11

𝟁(x)=sqrt(2/a)sin((nπx)/a)

Question 12

𝟁(x)=sqrt(2/a)sin((nπx)/a)

Answer 12

equation for particle in a box

Question 13

Purpose of n in the box’ed particle equation.

Answer 13

The edges of the box must equal zero, so only certain energy states can be used

Question 14

The edges of the box must equal zero, so only certain energy states can be used

Answer 14

Purpose of n in the box’ed particle equation.

Question 15

zero point energy

Answer 15

the lowest energy state (n) a particle in a box can occupy, can’t actualy be 0

Question 16

the lowest energy state (n) a particle in a box can occupy, can’t actualy be 0

Answer 16

Zero point energy

Question 17

to find the probability in a particle being in a certain part of the box

Answer 17

integrate psi squared from 0 to target

Question 18

integrate psi squared from 0 to target

Answer 18

to find the probability in a particle being in a certain part of the box

Question 19

Everything is in a box

Answer 19

in the real universe, everything is under some sort of constraint

Question 20

in the real universe, everything is under some sort of constraint

Answer 20

Everything is in a box

Question 21

Energy of a quantum step in a box

Answer 21

h^2n^2/8ma^2

Question 22

h^2n^2/8ma^2

Answer 22

Energy of a quantum step in a box

Question 23

scaling particle in a box to clasical

Answer 23

as the partigle grows it’s mass grows and the minimum size of the box also grows, since m and a^2 are on the bottom the gap between n’s shrinks to indistinguishable.

Question 24

as the partigle grows it’s mass grows and the minimum size of the box also grows, since m and a^2 are on the bottom the gap between n’s shrinks to indistinguishable.

Answer 24

scaling particle in a box to clasical

Question 25

When a particle hits an infinite barrier that it has enough energy to pass through

Answer 25

Transmittance is high, but the chance of reflection is never zero

Question 26

Transmittance is high, but the chance of reflection is never zero

Answer 26

When a particle hits an infinite barrier that it has enough energy to pass through

Question 27

transmittance for a high energy particle against an infinite barriar

Answer 27

T=(4k_2^2)/(k_1+k_2)^2 (where k is the wave vector magnitude)

Question 28

T=(4k_2^2)/(k_1+k_2)^2 (where k is the wave vector magnitude)

Answer 28

transmittance for a high energy particle against an infinite barriar

Question 29

Reflectance for a high energy particle against an infinite barriar

Answer 29

R=(k_1-k_2)^2/(k_1+k_2)^2 (where k is the wave vector magnitude)

Question 30

R=(k_1-k_2)^2/(k_1+k_2)^2 (where k is the wave vector magnitude)

Answer 30

Reflectance for a high energy particle against an infinite barriar

Question 31

When a particle hits an infinite barrier and doesn't have enough energy to pass through

Answer 31

it will always be reflected, but it has a chance of penitrating into the barrier before turning around.

Question 32

it will always be reflected, but it has a chance of penitrating into the barrier before turning around.

Answer 32

When a particle hits an infinite barrier and doesn't have enough energy to pass through

Question 33

when a particle with greter anergy than a barrier hit a non-infinite barriar

Answer 33

the particle still has a small chance of reflection, but it will most likely be transmitted to the other side, with the same waveleingth but different amplitude

Question 34

the particle still has a small chance of reflection, but it will most likely be transmitted to the other side, with the same waveleingth but different amplitude

Answer 34

when a particle with greter anergy than a barrier hit a non-infinite barriar

Question 35

Transmittance for a high energy particle and a non-infinite barriar

Answer 35

T=[1+(((sin^2(𝜒*√(ε -1))/(4ε (ε -1)))]^-1

Question 36

T=[1+(((sin^2(𝜒*√(ε -1))/(4ε (ε -1)))]^-1

Answer 36

Transmittance for a high energy particle and a non-infinite barriar

Question 37

Reflectance for a high energy particle and a non-infinite barriar

Answer 37

R=[1+(4ε (ε -1))/(sin^2(𝜒*√(ε -1))]^-1

Question 38

R=[1+(4ε (ε -1))/(sin^2(𝜒*√(ε -1))]^-1

Answer 38

Reflectance for a high energy particle and a non-infinite barriar

Question 39

value of epsilon

Answer 39

ε=E/V_o

Question 40

ε=E/V_o

Answer 40

value of epsilon

Question 41

value of Chi

Answer 41

𝜒=(a√2mV_o)/h

Question 42

𝜒=(a√2mV_o)/h

Answer 42

value of Chi

Question 43

Transmission resonance

Answer 43

when the energy of the particle is equal to specific values, transmitance is extremely high (1) becaue of resonance while inside the barriar

Question 44

when the energy of the particle is equal to specific values, transmitance is extremely high (1) becaue of resonance while inside the barriar

Answer 44

Transmission resonance

Question 45

Equation for Transmission resonance

Answer 45

E=V_o+(h^2n^2)/(8ma^2

Question 46

E=V_o+(h^2n^2)/(8ma^2

Answer 46

Equation for Transmission resonance