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Chem 324 VENGEANCE > Uncertainty, Probability, & Normality > Flashcards

Uncertainty, Probability, & Normality Flashcards

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1
Q

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

A

Quantum mechanics

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2
Q

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

A

Quantum mechanics

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3
Q

Quantum mechanics is based on several statements called __________.

A

postulates

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4
Q

These postulates are ________, not proven

A

assumed

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5
Q

Why do we believe these postulates even if not proven?

A

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

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6
Q

The wavefunction contains ___________.

A

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

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7
Q

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

A

arbitrary

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8
Q

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

A

time-dependent Schrödinger equation.

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9
Q

Quantum mechanics predicts values that __________________________________.

A

agree with experimentally determined measurements

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10
Q

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

A

wavefunction

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11
Q

What are the limitations of a wavefunction?

A

single valued, continuous, bounded, differentiable/integrable

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12
Q

Functions that meet all these criteria are considered _______________________.

A

acceptable wavefunctions

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13
Q

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

A

derived from the wavefunction

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14
Q

Give examples of an observable.

A

mass, volume, position, momentum, and energy

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15
Q

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

A

to perform some mathematical operation on a wavefunction

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16
Q

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

A

eigenvalue equation

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17
Q

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

A

physical observable
operator

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18
Q

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

A

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

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19
Q

The eigenvalue equation is constructed from the ____________________.

A

the operator and the wavefunction

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20
Q

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

A

real numbers

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21
Q

Heisenberg’s full name

A

Werner Karl Heisenberg

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22
Q

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

A

Heisenberg’s uncertainty
principle

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23
Q

Hermitian operators are operators that always have ____________________ as eigenvalues .

A

real (nonimaginary) numbers

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24
Q

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

A

because in order to be observed a quantity must be real

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25
Q

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

A

Charles Hermite

26
Q

When did Werner Karl Heisenberg announce his uncertainty principle?

A

1927

27
Q

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

A

limits

28
Q

The de Broglie wavelength is related to a _______________.

A

momentum

29
Q

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

A

position and momentum

30
Q

The uncertainty principle puts a ____________ on the uncertainty.

A

lower bound

31
Q

Full name of German scientist Born

A

Max Born

32
Q

dT is called?

A

infinitesimal of integration

33
Q

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

A

definite region

34
Q

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

A

probability of the location of an electron

35
Q

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%

A

entire space

36
Q

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

A

normalized

37
Q

The ___________________ does not affect the shape of the function.

A

normalization constant

38
Q

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

A

Postulate 1

39
Q

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

A

Postulate 2

40
Q

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

A

Postulate 3

41
Q

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

A

Postulate 4

42
Q

The Heisenberg’s uncertainty principle states that states that it is __________.

A

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

43
Q

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__________.

A

certain region

44
Q

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 ________________

A

1 or 100%.

45
Q

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

A

limits
limits

46
Q

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

A

normalization constant

47
Q

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

A

all space

48
Q

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

A

normalization constant

49
Q

___________________ deals with the most important observable: energy

A

The Schrödinger Equation

50
Q

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

A

Erwin Schrödinger

51
Q

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

A

Hamiltonian function

52
Q

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

A

stationary state

53
Q

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

A

energies of the systems

54
Q

The behavior of electrons is described by a ___________________.

A

wavefunction

55
Q

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

A

Hamiltonian operator

56
Q

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

A

kinetic
potential

57
Q

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

A

analytic solutions

58
Q

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.

A

the particle-in-a-box

59
Q

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

A

zero
infinity

60
Q

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

A

boundary condition

61
Q

It is referred to as the three-dimensional operator.

A

Laplacian operator

62
Q
A

Chem 324 VENGEANCE (10 decks)

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