For the following functions and operators, determine if the given function is an eigenfunction of the operator. If the function is an eigenfunction, determine the eigenvalue of the operator. a. Ĥ (V=0), y = A sin(nx²)

For the following functions and operators, determine if the given function is an eigenfunction of the operator. If the function is an eigenfunction, determine the eigenvalue of the operator. a. Ĥ (V=0), y = A sin(nx²)

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter10: Introduction To Quantum Mechanics

Section: Chapter Questions

Problem 10.40E

See similar textbooks

Related questions

Q: 1.613 g sample of an unknown nonionizing molecular compound is added to 250.0 g of benzene (C6H6, MW…

A: The depression in freezing point of Benzene, Tf =T0-Tf = 0.17 oCFor benzene, Kf = 1.86 oC.m-1 Mass…

Q: What is the relationship between the following two compounds? Answer: Check он он Answer: What is…

A: Given,The compounds:

Q: Please draw structure using ChemDraw. Thank you!! 1. (S)-2,3-epoxypropan-1-ol with sodium cyanide…

A: nucle

Q: Nitrogen dioxide (NO₂) gas and liquid water (H₂O) react to form aqueous nitric acid (HNO3) and…

A: We need to balance the given reaction. The reaction is :NO>2(g) + H2O (l) --> HNO3 (g) + NO…

Q: Predict which reaction would react faster. Provide an explanation for your prediction. OH + (+) LOH…

Q: Add any missing formal charges to the product of the organic chemical reaction below. If there is…

A: A formal charge is a charge assigned to an atom in a molecule, assuming that all electrons in the…

Q: Rank the following molecules in order of least to most soluble in water: NaNO3 CH3CH2OH…

A: Solubility is a fundamental concept in chemistry that refers to the ability of one substance (the…

Q: Convert 10.4 gargs into meters if 492 garg = 23.9 bales and 5 bales = 300.0 meters.

A: The conversion of quantity from one unit system to another unit system is known as unit conversion.…

Q: What type of compound is most consistent with the IR spectrum shown below? LOD 50 D 4000 3000 O…

A: The given IR spectrum is shown belowWe have to identify which type of compound is most consistent…

Q: nswer choices for all 4: terminal alkyne ester aldehyde carboxylic acid alcohol internal…

A: IR spectroscopy is mainly used for the identification of functional groups present in the organic…

Q: When Uranium-235 is bombarded with a single neutron, the following fission reaction occurs: Find x,…

A: Tectinium - 99m - Technetium-99m is used to image the skeleton and heart muscle in particular, but…

Q: Give detailed mechanism Solution with explanation needed..don't give Handwritten answer

A: Dehydration is the removal of water molecules from the alcohol which produces the double bond. This…

Q: Briefly describe and compare Fisher carbene and Schrock carbene complexes. Illustrate your answer…

A: Carbenes :CH2, :CHR , :CR2 , are rarely stable in free state. They are both thermodynamically and…

Q: Be sure to answer all parts. Give the IUPAC name for the following compound: (select) (select)…

A: IUPAC nomenclature: In IUPAC nomenclature a molecule's longest chain of carbon is taken as parent…

Q: Consider the reaction Cu²+ + e = Cut which has an equilibrium standard potential of 0.153 V (SHE).…

A: where,

Q: How many moles of atoms are in a pure gold ring (24K) that has a mass of O 6.62 mol O 399 x 1024 mol…

A: Mass = 6.62 gmAtomic mass of gold (Au) = 196.97 g/mole

Q: Can you please help me with number 3

A: Dimethyl ether can be prepared by Williamson's ether reaction. In this reaction, sodium…

Q: 4. Calculate at which Zn² concentration (x) the following electrochemical cell has an EMF of 0.9 V.…

Q: Which statement is true regarding Kw? 1 [H₂O+][OH The value of Kw is temperature dependent. Kw More…

A: 1. Kw = 1 / [H3O+][OH-] - This statement is incorrect. Kw is the ion product of water and is equal…

Q: O STATES OF MATTER Applying like dissolves like HO- : 0: || HO-C- OH I solute : 0: || CH-CH₂-C-OH I…

A: Like dissolves like.Polar substances soluble in polar solventsNon-polar substances soluble in…

Q: 4. How many electrons would be transferred in the redox reaction below as balanced? 6 Cu(NO3)2(aq) +…

A: Redox reaction is defined as a reaction in which oxidation and reduction take place simultaneously.…

Q: 1. A solution containing water (H2O) and ethanol (CH3CH2OH) has an initial mole concentration…

A: The solution is heated to the boiling point of ethanol (78.4 °C). The vapor pressure of water at…

Q: Draw the structure of the product of the Diels-Alder reaction below. CH3 a CH3 + 8 CH3OC-C=C-COCH3…

Q: Choose all lewise acids below: HCI A 00000 ABCDF А CH3 CH3 B CH3 CH3NCH3 C Ti4+ D BC13 E

A: Lewis acids are those species which have incomplete octate or simply have vacant orbitals to accept…

Q: Why did you add 3 electrons to the Bismuth equation if the solid had no charge and the right side…

A: Answer:During a chemical reaction when a specie loses electrons and its oxidation number increase…

Q: CH3ONa + CH3I → CH3OCH3 + NaI Please draw the structure using CHEMDRAW

A: A reaction is given. we have to draw the structures of the compounds in the reaction.

Q: Consider the reaction Cu²+ + e = Cut which has an equilibrium standard potential of 0.153 V (SHE).…

A: where,

Q: How are these molecules related? A) identical (B) diastereomers H. OH H Br CH3 (C) enantiomers OH Br…

A: three dimensional molecules can be represented in many ways called projections.

Q: Consider the following NAS reaction. Show the corresponding intermediate - include all reasonable…

A: The given reaction is an example of nucleophilic aromatic substitution.The reactant is…

Q: If too much drying agent is added to a solution, what can be done to correct the situation?

A: Drying agent is used to remove trace amounts of water from an organic solution.There is no set rule…

Q: Match terms of AG, AG, and AG'with the statements that best describes them. Use each term only once.…

A: Free energy is the energy available to perform work.

Q: Balance the following chemical reaction 3. For basic conditions Cu + NO3 → Cu+² + NO₂

Q: Give the Lewis dot symbol for the following elements and explain how this relates to the expected…

A: Lewis structure is a diagrammatic representation of molecules in which bonding and non bonding (lone…

Q: How can collision-reaction theory explain the effect of temperature on the rate of the reaction?

A: The collision reaction theory states that a chemical reaction can only occur between particles when…

Q: Identify all carbon atoms and missing hydrogen atoms for the following compounds. Provide the…

A: Carbon can form maximum of 4 bonds, oxygen can form maximum of 2 bonds.

Q: 17. 33.32 g of XY contains 10.25 g of X. Its other component is Y. How many grams of Y are in a…

A: • First sample of XY,mass of XY = 33.32 gmass of X = 10.25 g• Second sample of XY,mass of XY = 20.00…

Q: Indicate a condensed structural formula for the following compound: OH

A: There are various ways of representation of the organic compounds- 1- bond-line structure2-…

Q: what percent of FeSO4 times 6H2O i

A: To determine the percentage of iron (Fe) in FeSO4•6H2O (iron(II) sulfate hexahydrate), you need to…

Q: Draw all four carbocation intermediates possible upon protonation of the diene below. Draw all…

Q: Select the single best answer. Choose the chair conformation of cyclohexane with one CH3CH₂ group…

A: We know in cyclohexane chair form bulky groups are generally present at equatorial position to…

Q: Complete the statement to make it TRUE. When an ionic salt such as NaCl is dissolved in water .....…

A: Answer:Decrease in net energy content causes an increase in stability of the system and increase in…

Q: 2. For each of the indicated bonds, label the type of bond and the atomic/hybrid orbitals that…

A: Sigma bonds are formed by end to end overlap between hybrid orbitals or atomic orbitals or…

Q: The molal boiling point elevation constant K=1.23 °C-kg-mol solution boils at 114.3 °C. Calculate…

A: Given,The mass of substance X = 250. gThe mass of urea ( (NH2)2CO ) =10. gThe boiling point of the…

Q: Consider the system represented below which can exist in two different states. Which conditions of…

A: The gases are soluble in liquid and the solubility of a gas in a liquid depends on the nature of gas…

Q: Pick the measurements below that are precise but not accurate for the density of water, 1.000 g/mL.…

A: Accuracy: It refers to how close a measurement is to the true or accepted value. Precision: It…

Q: 120.0 J is added to 12.0 g of aluminum originally at 25.0 o C, what will the new temperature be?

A: Given,The heat absorbed by aluminum = 120.0 Jmass of aluminum = 12.0 gInitial temperature = 25.0…

Q: Alpha-phellandrene, C₁0H₁6, is a pleasant-smelling chiral compound that may be obtained from the…

A: The molecular formula of the Alpha-phellandrene is C10H16.The hydrogenation of it by palladium…

Q: Oseltamivir, the most effective antiviral drug against avian influenza currently available, can be…

A: Identify functional groups in the following reactant and product:

Q: MISSED THIS? Watch KCV: The Mole Concept, IWE: The Mole Concept Converting between Mass and Number…

A: Given, The mass of 3.89 x 1023 atoms of an element = 20.0 g

Q: 6. Determine the standard potential (Az* = 1M) for the reaction: Az* +e™ = Az (a) 0.400 V. (b) 0.500…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Concept explainers

Quantum Chemistry

Quantum chemistry deals with the properties of chemical systems and their reactions. The branch of chemistry which is more concerned with quantum chemistry is physical chemistry. It is a more sophisticated field of theoretical physics which is concerned towards the application of physical concepts towards various chemical aspects such as, formation of atoms, chemical structure descriptions, chemical bond strength, hybridization, conjugation etc. Quantum chemistry mainly studies the various states i.e., ground state, excited state, transition states of the individual atoms or molecules taking place during any chemical reaction. The laws of motion explained by various scientists, which are termed as “classical mechanics” were not acceptable in terms of electrons, protons, atoms, light etc. Thus, a new theory named “quantum mechanics” emerged to understand the basic framework of various atomic and subatomic particles.

Question

2.
For the following functions and operators, determine if the given function is an
eigenfunction of the operator. If the function is an eigenfunction, determine the
eigenvalue of the operator.
a. Ĥ (V=0), y = A sin(nx²)
b. p, y=B exp{-ikx}
c. x, y = c ( 1⁄₂ - 1)
C
ə
ô - (ax + by), w
=
дх
d. ô
y = K x²y²

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Guideline message

VIEW

Step 2: Determine whether the given function is eigen function or not

VIEW

Step 3: Determine whether the given function is eigen function or not

VIEW

Step 4: Determine whether the given function is eigen function or not

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Introduction and Principles of Quantum Theory

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.

Similar questions

What is the physical explanation of the difference between a particle having the 3-D rotational wavefunction 3,2 and an identical particle having the wavefunction 3,2?
2.) The function, f(x) = 3X² - 1, is an eigenfunction of the operator, A = - (1- x)(d²/ dx²) + 2x(d /dx). Find the eigenvalue corresponding to this eigenfunction.
Demonstrate that the function y = exp(timx) is simultaneously eigenfunction of an d P=-i dx and
Is the function w(x) = sinx an eigenfunction for the linear momentum operator, 6.? If yes, what is the eigenvalue? O Yes, the eigenvalue is -1 Yes, the eigenvalue is sinx O Yes, the eigenvalue is – in O No
You are given a free particle (no potential) Hamiltonian ÎI - dependent wave-functions = ₁(x, t) V₂(x, t) = -it 2h² m = ħ² d² 2m dx2 sin(27x)e-it 2 sin(x)eit + sin(2x)e¯ hn 2 • Are V₂(x, 0) eigenfunctions of Ĥ ? (give explanation for each case) and two time- -it 2hr 2 m (1) (2)
3) Consider an arbitrary operator A. A operates on any function to its right. Here are the results of this operator on three different functions: Af(x, y, z) = hf(x, y, z) AY(0) = 04(0) ÂY(x) = Y(x) Which of the functions are eigenfunctions of Â?
4) Is the function = B sin (bx) an eigenfunction of the operator d/dx = = d/dx if B and b are constants and real numbers? Show your work in detail.
Consider the operators d/dx and d²/dx². Is y (x) Aeikx an +Be-ikx eigenfunction of these operators? If so, what are the eigenvalues? A, B, and k are real numbers. =
(5) Demonstrate that the function p=-; d dx y = exp(timx) is simultaneously an eigenfunction of and p²
d? A = 4x² 3. Given the operator dx? determine the value of k that makes the wave function v (x)= e** an eigenfunction of 4
Consider the angular momentum operator Îz in coordinate representation L₂ = − iħ (x ² − y ²²x), a. express Î₂ in spherical coordinates. b. what are the (unnormalized) eigenfunctions? c. what normalization condition do these eigenfunction satisfy? d. what are the eigenvalues Lz?
Which of the following statements is false? ○ If operators A and B do not commute, an eigenfunction of A cannot be an eigenfunction of B. OYO is a constant. Y is an eigenfunction of L², Lx, Ly, and L₂. L² commutes with Ly. The eigenvalues of operator L² are degenerate except for I = 0.