Part 1 Flashcards
Quantum mechanics is based on several statements called__________
postulates
Are these postulates proven?
No, they are assumed not proven.
If not proven then why do we believe these postulates?
the reason is simply because the statements based on these assumptions lead to predictions about atoms and molecules that agree with our observations.
The behavior of electrons, by now known to have wavelike properties, can be described by a mathematical expression called a _____________.
wavefunction
It contains within it all possible information that can be known
about a system
wavefunction
wavefunctions are not ________ mathematical functions, but must satisfy certain simple conditions
arbitrary
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 predicts values that agree
with experimentally determined measurements
Quantum mechanics
It is the simplest real system
hydrogen atom
It properly describes the behavior of matter, as determined
by observation.
Quantum mechanics
Quantum mechanics properly describes ___________________.
the behavior of matter, as determined by observation.
The behavior of a wave can be expressed as a simple mathematical function:
y= Asin (Bx + C) + D
How many postulates does quantum mechanics have?
6
How many postulates were discussed by Sir N?
There were 7. HAHAHAHA
What are the 7 postulates of Quantum Mechanics
- The state of a system of particles is given by a wavefunction.
- For every physical observable there exists a corresponding Hermitian Operator.
- The only values of observables that can be obtained in a single measurement are the eigenvalues of eigenvalue equation.
- Wavefunction must satisfy the time-dependent Schrodinger equation.
- The average value of an observable is given by an expression for normalized wavefunctions.
- The set of eigenfunctions for any quantum mechanical operator is complete mathematical set of functions.
- Superposition principle.
Guess which postulate
The only values of observables that can be obtained in a single measurement are the eigenvalues of eigenvalue equation.
Postulate 3
Guess which postulate
Wavefunction must satisfy the time-dependent Schrodinger equation.
Postulate 4
Guess which postulate
It tackles the superposition principle.
Postulate 7
Guess which postulate
For every physical observable there exists a corresponding Hermitian Operator.
Postulate 2
Guess which postulate
The state of a system of particles is given by a wavefunction.
Postulate 1
Guess which postulate
The set of eigenfunctions for any quantum mechanical operator is complete mathematical set of functions.
Postulate 6
Wavefunction in quantum mechanics is given the symbol __________.
psi (Ψ)
What are the 4 limitations to which wavefunctions are constrained?
- Single-valued
- Continuous
- Bounded
- Differentiable
____________ are constructed by writing their classical expression in terms of position and momentum.
Operators
It contains all information that can be determined about the state of the system.
wavefunction
How is an eigenvalue function and eigenvalue formed?
It is when an operator acts on a function and produces the original function multiplied by any constant.
A derivative with respect to position, not with respect to time as with the classical definition
Momentum operator
These are operators that always have real (nonimaginary) numbers as eigenvalues.
Hermitian operators
TRUE OR FALSE
The uncertainity priniciple isn’t limited to the position and momentum operators.
True
It makes obvious the necessity of wavefunctions being bounded and single-valued
The Born interpretation
What happens when a wavefunction is not bounded
It approaches infinity
Can probabilities be infinite? Yes or No
NO
Why must a wavefunction be single-valued
Because **probability ** of existence represents a physical observable, it must have a specific value; therefore,Ψ’s (and their squares) must be single-valued.
The Born interpretation also requires that a probability be evaluated over a _________________.
definite region
A state whose probability distribution, related to by the Born interpretation, does not vary with time.
Stationary state
Why does a wavefunction get normalized?
According to the Born
interpretation of Ψ, normalization also guarantees that the probability of a particle existing in all space is 100%.
The Schrodinger equation deals with the observable ___________.
Energy
The Schrodinger equation is based on what?
The Hamiltonian function
What do you call the operator for energy that Schrodinger derived?
Hamiltonian operator
The eigenvalue of the Hamiltonian operator corresponds to the __________.
total energy
What does the Schrodinger equation yield when to ideal and real systems.
It yields the values for the energies of the systems.
the wavefunction must be a certain value at the boundaries of the system, is called a ________________.
boundary condition
as one goes to higher and higher quantum numbers, the plot of Ψ^2 can be approximated as some constant probability.
correspondence principle
A general system, showing a box having its origin at (________) and having dimensions a x b x c
0,0,0
values of V inside the box and V outside the box.
V inside= 0
V outside= infinity
What do you particularly call dx, dy, and dz?
infinitesimals
When the system is ________________ the quantum numbers and the lengths might be such that different sets of quantum numbers nx, ny, nz would yield the same energy for the two different wavefunctions
Symmetric
If a set of three quantum numbers adds up to the same total as another set of three different quantum numbers, or if the quantum numbers themselves exchange values, the energies would be exactly the same even though the wavefunctions are different.
degeneracy
Different, linearly independent wavefunctions that have the same energy are called ______________.
degenerate
TRUE OR FALSE
Degenerate wavefunctions may have different eigenvalues of other observables.
TRUE
The corresponding wavefunctions have no common quantum numbers, but their energy eigenvalues are exactly the same
accidental degeneracy
