Quantum chem

Question 1

Quantum mechanics is based on several statements called _______________.

Answer 1

postulates

Question 2

TRUE or FALSE
These postulates are proven.

Answer 2

FALSE
These postulates are assumed, not proven

Question 3

If these postulates are not proven then why do we base an entire model based on these assumptions?

Answer 3

the statements based on these assumptions lead to predictions about atoms and molecules that agree with our observations

Question 4

The _____________________, by now known to have wavelike properties, can be described by a mathematical expression called a wavefunction.

Answer 4

behavior of electrons

Question 5

The wavefunction contains within it all _____________________________________.

Answer 5

possible information that can be known about a system.

Question 6

Wavefunctions are __________ mathematical functions, but must satisfy certain simple conditions

Answer 6

not arbitrary or UNARBITRARY

Question 7

An arbitrary function simply means that it is ______________________________________. The simple constraint is that it should be a function

Answer 7

a function that you are free to define in any way you want

Question 8

The most important condition is that the wavefunction must satisfy ________________________________.

Answer 8

the time-dependent Schrödinger equation

Question 9

Quantum mechanics predicts values that ________________________________________.

Answer 9

agree with experimentally determined measurements.

Question 10

It is a system that Rydberg and Balmer and Bohr had studied with different degrees of success.

Answer 10

Hydrogen atom

Question 11

y = A sin (Bx + C) + D is a general expression for the _________.

Answer 11

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.

Question 12

The first postulate of quantum mechanics

Answer 12

is that the state of a system can be described by an expression called a wavefunction.

Question 13

What are the limitations/conditions of a wavefunction???

Answer 13

1. Single-valued
   wavefunction must have only one possible f(x) value for each and every value of x.
2. Continuous
3. Differentiable
   there must be no mathematical reasons why the derivative of Ψ cannot exist.
4. Bounded
   prohibits functions that approach either positive or negative infinity, except maybe for individual points in the function
5. Square-integrable

Question 14

What is an observable?

Answer 14

Observable in physics is a quantity that can be measured or directly inferred from experimental data.

Question 15

Examples of observables

Answer 15

Mass, position, volume, momentum, and energy

Question 16

Second postulate of quantum mechanics states that

Answer 16

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

Question 17

In other words, an operator acts on a function (or functions) to ______________.

Answer 17

produce a function.

Question 18

The eigenvalue equations that we will consider have ______________ as values of eigenvalues

Answer 18

real numbers

Question 19

When an operator acts on a function
and produces the original function multiplied by any constant ______________ is produced.

Answer 19

EIGENVALUE EQUATION

Question 20

TRUE OR FALSE
Not all functions are eigenfunctions of all operators.

Answer 20

TRUE

Question 21

A function that remains unchanged (up to a constant factor) when the operator is applied to it.

Answer 21

EIGENFUNCTION

Question 22

POSTULATE 1

Answer 22

The state of a system of particles is given by a wavefunction.

Question 23

POSTULATE 2

Answer 23

For every physical observable or variable, there exists a corresponding Hermitian operator.

Question 24

POSTULATE 3

Answer 24

The only values of observables that can be obtained in a single measurement are the eigenvalues of an eigenvalue equation.

Question 25

POSTULATE 4

Answer 25

Wavefunctions must satisfy the time-dependent schrodinger equation.