Quantum chem Flashcards
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Quantum mechanics is based on several statements called _______________.
postulates
TRUE or FALSE
These postulates are proven.
FALSE
These postulates are assumed, not proven
If these postulates are not proven then why do we base an entire model based on these assumptions?
the statements based on these assumptions lead to predictions about atoms and molecules that agree with our observations
The _____________________, by now known to have wavelike properties, can be described by a mathematical expression called a wavefunction.
behavior of electrons
The wavefunction contains within it all _____________________________________.
possible information that can be known about a system.
Wavefunctions are __________ mathematical functions, but must satisfy certain simple conditions
not arbitrary or UNARBITRARY
An arbitrary function simply means that it is ______________________________________. The simple constraint is that it should be a function
a function that you are free to define in any way you want
The most important condition is that the wavefunction must satisfy ________________________________.
the time-dependent Schrödinger equation
Quantum mechanics predicts values that ________________________________________.
agree with experimentally determined measurements.
It is a system that Rydberg and Balmer and Bohr had studied with different degrees of success.
Hydrogen atom
y = A sin (Bx + C) + D is a general expression for the _________.
for the amplitude, y, of a sine-type (or sinusoidal) wave traveling in the x dimension. The constants A, B, C, and D have certain values that specify exactly what the sine wave looks like.
The first postulate of quantum mechanics
is that the state of a system can be described by an expression called a wavefunction.
What are the limitations/conditions of a wavefunction???
-
Single-valued
wavefunction must have only one possible f(x) value for each and every value of x. - Continuous
-
Differentiable
there must be no mathematical reasons why the derivative of Ψ cannot exist. -
Bounded
prohibits functions that approach either positive or negative infinity, except maybe for individual points in the function - Square-integrable
What is an observable?
Observable in physics is a quantity that can be measured or directly inferred from experimental data.
Examples of observables
Mass, position, volume, momentum, and energy
Second postulate of quantum mechanics states that
In order to determine the value of an observable, you have to perform some mathematical operation on a wavefunction. This operation is represented by an operator
In other words, an operator acts on a function (or functions) to ______________.
produce a function.
The eigenvalue equations that we will consider have ______________ as values of eigenvalues
real numbers
When an operator acts on a function
and produces the original function multiplied by any constant ______________ is produced.
EIGENVALUE EQUATION
TRUE OR FALSE
Not all functions are eigenfunctions of all operators.
TRUE
A function that remains unchanged (up to a constant factor) when the operator is applied to it.
EIGENFUNCTION
POSTULATE 1
The state of a system of particles is given by a wavefunction.
POSTULATE 2
For every physical observable or variable, there exists a corresponding Hermitian operator.
POSTULATE 3
The only values of observables that can be obtained in a single measurement are the eigenvalues of an eigenvalue equation.
POSTULATE 4
Wavefunctions must satisfy the time-dependent schrodinger equation.