Wavefunctions Flashcards
Born interpetation
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.
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.
Born interpetation
finding the probability that a particle will be in a certain area
integrate the squared wave equation over the are in questin
integrate the squared wave equation over the are in questin
finding the probability that a particle will be in a certain area
normalizing a wave function
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
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
normalizing a wave function
requirments for born interpetaion
no jumping to infinity, no more than one value per space, and both the equation and it’s derivative must be continuous.
no jumping to infinity, no more than one value per space, and both the equation and it’s derivative must be continuous.
requirments for born interpetaion
wave packet
a representation of the area where a quantum partical could be. Marking one spot makes it look like a clasical particle.
a representation of the area where a quantum partical could be. Marking one spot makes it look like a clasical particle.
wave packet
equation for a particle in a box
𝟁(x)=sqrt(2/a)sin((nπx)/a)
𝟁(x)=sqrt(2/a)sin((nπx)/a)
equation for particle in a box
Purpose of n in the box’ed particle equation.
The edges of the box must equal zero, so only certain energy states can be used
The edges of the box must equal zero, so only certain energy states can be used
Purpose of n in the box’ed particle equation.
zero point energy
the lowest energy state (n) a particle in a box can occupy, can’t actualy be 0
the lowest energy state (n) a particle in a box can occupy, can’t actualy be 0
Zero point energy
to find the probability in a particle being in a certain part of the box
integrate psi squared from 0 to target
integrate psi squared from 0 to target
to find the probability in a particle being in a certain part of the box
Everything is in a box
in the real universe, everything is under some sort of constraint
in the real universe, everything is under some sort of constraint
Everything is in a box
Energy of a quantum step in a box
h^2n^2/8ma^2
h^2n^2/8ma^2
Energy of a quantum step in a box
scaling particle in a box to clasical
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.
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.
scaling particle in a box to clasical
When a particle hits an infinite barrier that it has enough energy to pass through
Transmittance is high, but the chance of reflection is never zero
Transmittance is high, but the chance of reflection is never zero
When a particle hits an infinite barrier that it has enough energy to pass through
transmittance for a high energy particle against an infinite barriar
T=(4k_2^2)/(k_1+k_2)^2 (where k is the wave vector magnitude)
T=(4k_2^2)/(k_1+k_2)^2 (where k is the wave vector magnitude)
transmittance for a high energy particle against an infinite barriar
Reflectance for a high energy particle against an infinite barriar
R=(k_1-k_2)^2/(k_1+k_2)^2 (where k is the wave vector magnitude)
R=(k_1-k_2)^2/(k_1+k_2)^2 (where k is the wave vector magnitude)
Reflectance for a high energy particle against an infinite barriar
When a particle hits an infinite barrier and doesn’t have enough energy to pass through
it will always be reflected, but it has a chance of penitrating into the barrier before turning around.
it will always be reflected, but it has a chance of penitrating into the barrier before turning around.
When a particle hits an infinite barrier and doesn’t have enough energy to pass through
when a particle with greter anergy than a barrier hit a non-infinite barriar
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
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
when a particle with greter anergy than a barrier hit a non-infinite barriar
Transmittance for a high energy particle and a non-infinite barriar
T=[1+(((sin^2(𝜒*√(ε -1))/(4ε (ε -1)))]^-1
T=[1+(((sin^2(𝜒*√(ε -1))/(4ε (ε -1)))]^-1
Transmittance for a high energy particle and a non-infinite barriar
Reflectance for a high energy particle and a non-infinite barriar
R=[1+(4ε (ε -1))/(sin^2(𝜒*√(ε -1))]^-1
R=[1+(4ε (ε -1))/(sin^2(𝜒*√(ε -1))]^-1
Reflectance for a high energy particle and a non-infinite barriar
value of epsilon
ε=E/V_o
ε=E/V_o
value of epsilon
value of Chi
𝜒=(a√2mV_o)/h
𝜒=(a√2mV_o)/h
value of Chi
Transmission resonance
when the energy of the particle is equal to specific values, transmitance is extremely high (1) becaue of resonance while inside the barriar
when the energy of the particle is equal to specific values, transmitance is extremely high (1) becaue of resonance while inside the barriar
Transmission resonance
Equation for Transmission resonance
E=V_o+(h^2n^2)/(8ma^2
E=V_o+(h^2n^2)/(8ma^2
Equation for Transmission resonance
