Uncertainty, Probability, & Normality

Question 1

It is described as a better theory to describe the behavior of matter at the atomic level.

Answer 1

Quantum mechanics

Question 2

It provides a theoretical background that makes predictions that agree with experiment.

Answer 2

Quantum mechanics

Question 3

Quantum mechanics is based on several statements called __________.

Answer 3

postulates

Question 4

These postulates are ________, not proven

Answer 4

assumed

Question 5

Why do we believe these postulates even if not proven?

Answer 5

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

Question 6

The wavefunction contains ___________.

Answer 6

within it all possible information that can be known about a system.

Question 7

Wavefunctions are not _________ mathematical functions, but must satisfy certain simple conditions

Answer 7

arbitrary

Question 8

The most important condition is that the wavefunction must satisfy the _________________

Answer 8

time-dependent Schrödinger equation.

Question 9

Quantum mechanics predicts values that __________________________________.

Answer 9

agree with experimentally determined measurements

Question 10

The state of a system can be described by
an expression called a __________________.

Answer 10

wavefunction

Question 11

What are the limitations of a wavefunction?

Answer 11

single valued, continuous, bounded, differentiable/integrable

Question 12

Functions that meet all these criteria are considered _______________________.

Answer 12

acceptable wavefunctions

Question 13

All possible information about the various observable properties of a system must be _______________________.

Answer 13

derived from the wavefunction

Question 14

Give examples of an observable.

Answer 14

mass, volume, position, momentum, and energy

Question 15

In order to determine the value of an observable, you have ______________.

Answer 15

to perform some mathematical operation on a wavefunction

Question 16

When an operator acts on a function and produces the original function multiplied by any constant the equation is referred to as an ____________.

Answer 16

eigenvalue equation

Question 17

Another postulate of quantum mechanics states that for every ______________ of interest, there is a corresponding ___________.

Answer 17

physical observable
operator

Question 18

The only values of the observable that will
be obtained in a single measurement must be _____________________-.

Answer 18

eigenvalues of the eigenvalue equation constructed from the operator and the wavefunction

Question 19

The eigenvalue equation is constructed from the ____________________.

Answer 19

the operator and the wavefunction

Question 20

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

Answer 20

real numbers

Question 21

Heisenberg’s full name

Answer 21

Werner Karl Heisenberg

Question 22

__________________ completely changed the way science understands the limitations in the ability to measure nature.

Answer 22

Heisenberg’s uncertainty
principle

Question 23

Hermitian operators are operators that always have ____________________ as eigenvalues .

Answer 23

real (nonimaginary) numbers

Question 24

All operators that yield quantum mechanical observables are Hermitian operators, ________________________.

Answer 24

because in order to be observed a quantity must be real

Question 25

Hermitian operators are named after _________________, a nineteenth century French mathematician

Answer 25

Charles Hermite

Question 26

When did Werner Karl Heisenberg announce his uncertainty principle?

Answer 26

1927

Question 27

The uncertainty principle states that there are ultimate _________ to how exact certain measurements can be

Answer 27

limits

Question 28

The de Broglie wavelength is related to a _______________.

Answer 28

momentum

Question 29

The uncertainty principle deals only with certain observables that might be measured simultaneously. Two of these observables are__________________.

Answer 29

position and momentum

Question 30

The uncertainty principle puts a ____________ on the uncertainty.

Answer 30

lower bound

Question 31

Full name of German scientist Born

Answer 31

Max Born

Question 32

dT is called?

Answer 32

infinitesimal of integration

Question 33

The Born interpretation also requires that a probability be evaluated over a ____________, not a specific point, in space.

Answer 33

definite region

Question 34

Instead of wavefunction giving the exact location of an electron, it will provide only the ________________________.

Answer 34

probability of the location of an electron

Question 35

If the probability for a particle having wavefunction were evaluated over the _____________________ in which the particle exists, then the probability should be equal to 1, or 100%

Answer 35

entire space

Question 36

In order to achieve 100% probability, a wavefunction must be ______________.

Answer 36

normalized

Question 37

The ___________________ does not affect the shape of the function.

Answer 37

normalization constant

Question 38

***STATE WHICH POSTULATE*** The state of a system of particles is given by a wavefunction.

Answer 38

Postulate 1

Question 39

***STATE WHICH POSTULATE*** For every physical observable or variable there exist a corresponding Hermitian operator.

Answer 39

Postulate 2

Question 40

***STATE WHICH POSTULATE*** The only values of observables that can be obtained in a single measurement are the eigenvalues of the eigenvalue equation.

Answer 40

Postulate 3

Question 41

***STATE WHICH POSTULATE*** Wavefunction must satisfy the time-dependent Schrodinger equation.

Answer 41

Postulate 4

Question 42

The Heisenberg’s uncertainty principle states that it is__________.

Answer 42

impossible for us to know simultaneously both the exact momentum of an electron and its exact location in space.

Question 43

It is very difficult to establish absolutely that a particular electron is in a particular place at a particular time. Rather, over a long period of time, the electron has a certain probability of being in a__________.

Answer 43

certain region

Question 44

If the probability for a particle having wavefunction were evaluated over the entire space in which the particle exists, then the probability should be equal to ________________

Answer 44

1 or 100%.

Question 45

The integral’s _______ would be modified to represent the ________ of the space a particle inhabits

Answer 45

limits limits

Question 46

wavefunctions must be multiplied by some constant, called the _____________, so that the area under the curve of Ψ* Ψ is equal to 1.

Answer 46

normalization constant

Question 47

According to the Born interpretation of Ψ, normalization also guarantees that the probability of a particle existing in ______________ is 100%.

Answer 47

all space

Question 48

It only imposes a scaling factor on the amplitude—a very convenient scaling factor.

Answer 48

normalization constant

Question 49

___________________ deals with the most important observable: energy

Answer 49

The Schrödinger Equation

Question 50

______________ proposed an expression of quantum mechanics that was different from but equivalent to Heisenberg’s.

Answer 50

Erwin Schrödinger

Question 51

The Schrödinger equation is based on the _____________________, because these equations naturally produce the total energy of the system:

Answer 51

Hamiltonian function

Question 52

If is a ________________ (that is, if its probability distribution Ψ does not depend on time), it must also satisfy the Schrödinger equation

Answer 52

stationary state

Question 53

When applied to ideal and even real systems, it yields the values for the ____________________________.

Answer 53

energies of the systems

Question 54

The behavior of electrons is described by a ___________________.

Answer 54

wavefunction

Question 55

The appropriate operator for predicting the energy of the electron is the ___________________.

Answer 55

Hamiltonian operator

Question 56

The ____________ energy part of the Hamiltonian has a similar form for all systems. However, the ___________ energy operator V^ depends on the system of interest

Answer 56

kinetic potential

Question 57

Solutions that have a specific mathematical form, either a number or an expression.

Answer 57

analytic solutions

Question 58

This is the first system for which there is an analytic solution is a particle of matter stuck in a one-dimensional “prison” whose walls are infinitely high barriers. What do you call this system.

Answer 58

the particle-in-a-box

Question 59

In the system particle-in-a-box, the potential energy inside the box itself is ___________. While outside it is _________.

Answer 59

zero infinity

Question 60

This requirement, that the wavefunction must be a certain value at the boundaries of the system, is called a _______________.

Answer 60

boundary condition

Question 61

It is referred to as the three-dimensional operator.

Answer 61

Laplacian operator

Question 62

As the mass of the object increases, the momentum increases, then the uncertainty __________.

Answer 62

decreases