5 postulates Flashcards
Postulate 1
A sum of all the particle’s behaviors can be represented by a wavefunction
A sum of all the particle’s behaviors can be represented by a wavefunction
Postulate 1
orthorombic wave functions
two wave functions are orthorombic if they equal zero when multipleid (and one of them is the imaginary coeficient)
two wave functions are orthorombic if they equal zero when multipleid (and one of them is the imaginary coeficient)
orthorombic wave functions
Orthonormal
the function(s) are both normalized and ortorombic
the function(s) are both normalized and ortorombic
Orthonormal
how to determine probabilities when the function is Orthonormal.
if the function s c*y than the probability of the partical being found in that range of locations is |c|^2
if the function s c*y than the probability of the partical being found in that range of locations is |c|^2
how to determine probabilities when the function is Orthonormal.
Postulate 2
by applying hermitian Operants to the wavefunction we can extract certain values
by applying hermitian Operants to the wavefunction we can extract certain values
Postulate 2
hermitian operant
an eigenfunction that alwasy gives a real eigenvalue
an eigenfunction that alwasy gives a real eigenvalue
hermitian operant
after completing the function, you get your input wavefunction as part of the output.
Eigenfunction
Eigenfunction
after completing the function, you get your input wavefunction as part of the output.
Eigenvalue
the valiue multiplying the wavefunction after competing an eigenfunction
the valiue multiplying the wavefunction after competing an eigenfunction
Eigenvalue
OPerator for position
x*wavefunction
x*wavefunction
Operator for position
Operator for 1d momentum
-iħ(d/dx)* wavefunction
-iħ(d/dx)* wavefunction
Operator for 1d momentum
Operator for kinetic energy
-ħ^2/2m d^2/dx^2
-ħ^2/2m d^2/dx^2
Operator for kinetic energy
Postulate 3
when you take a measuremnt you can only mesure something that is an eigenvalue of the appropriate opportator.
when you take a measuremnt you can only mesure something that is an eigenvalue of the appropriate opportator.
Postulate 3
if a wavefunction is an eigenvalue of the operator
we will always measure the same value if
we will always measure the same value if
if a wavefunction is an eigenvalue of the operator
If a wavefunction is not an eigenvalue of the operator
we will measure one of several different values if
we will measure one of several different values if
If a wavefunction is not an eigenvalue of the operator
Postulate 4
The probability of getting result A from a measurment of a wavefunction (where we apply operator Ahat) is given by |c|^2 (where c is added to the function for the purpose of weighting the probabilities)
The probability of getting result A from a measurment of a wavefunction (where we apply operator Ahat) is given by |c|^2 (where c is added to the function for the purpose of weighting the probabilities)
Postulate 4
The average of all measurements of A
<a>=sum(|c|^2a) where A is one of the possible eigenvalue measurments, and c is the coeficient for the probability of that measurement.</a>
<a>=sum(|c|^2a) where A is one of the possible eigenvalue measurments, and c is the coeficient for the probability of that measurement.</a>
The average of all measurements of A
commutive operators
measuring the wavefunction with one operator will not signifcantly change the wavefunction to measure the other operators
measuring the wavefunction with one operator will not signifcantly change the wavefunction to measure the other operators
commutive operators
physical commutive propery
we can determine both properties of the particle at the same time
non-comutive functions
measuring one value changes the function, so we cannot determine both at once, this is what causes the uncertainty principle.
measuring one value changes the function, so we cannot determine both at once, this is what causes the uncertainty principle.
non-comutive functions
Determining if two functions are commutive
if P[T𝟁(x)]-T[P𝟁(x)]=0 than the two opperators are commutive.
Postulate 5
schrodinger’s equation governs the change in an equation over time
schrodinger’s equation governs the change in an equation over time
Postulate 5
