Particle of mass m moves in a three-dimensional box with edge lengths L1, L2, and L3. (a) Find the energies of the six lowest states if L1 =L, L2 = 2L, and L3 = 2L. (b) Which if these energies are degenerate?

Particle of mass m moves in a three-dimensional box with edge lengths L1, L2, and L3. (a) Find the energies of the six lowest states if L1 =L, L2 = 2L, and L3 = 2L. (b) Which if these energies are degenerate?

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter8: Quantum Mechanics In Three Dimensions

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: 1/2 Question 13 One end of a cylindrical pipe has a radius of 1.5 cm. Water (density = 1.0x10^3…

Q: Given data: Distance to covered by car-22 m Time to cover the distance=25 Find speed

A: Given: The distance taveled by the car is 22 m. The time taken by the car is 2 s.

Q: a) A coil with 50 turns of wire is wrapped around a tube with a cross-sectional area of 0.25 m^2. A…

A: In the given question, Number of turns in the coil (n) = 50 Cross-sectional area of the coil (A) =…

Q: A man exerts a force of 50 N to push a 150 N box up a plane 4.0 m long on to a platform 1.0 m above…

Q: A 6.1-kg box sits on a flat table. You pull it straight up with a force of 17 N but the box doesn't…

A: For equilibrium net force acting on the body must be zero and horizontal as well as vertical forces…

Q: 5. The force of gravity acting on an object at four Earth radii from Earth's centre is 500 N. At a…

Q: Two cars started at the same point but at different times (of the same day) and at different speeds.…

A: Given data: Starting time of Car A tA = 9:00 am Speed of car A vA = 30 kph west Starting time of Car…

Q: Grace ran 18.084 km in 1.000 h, a world record time. If her kinetic energy was 694 J, what was her…

A: Given Data : The distance traveled by Grace is given as d = 18.084 Km = 18084 m. The time taken by…

Q: The pressure exerted on the ground by a man is greatest when: O all of the other choices yield the…

A: Pressure - Force per unit perpendicular area is the pressure. So when the area is minimum then the…

Q: A tennis ball connected to a string of radius 0.80 m is spun around in a vertical, circular path at…

A: Given, Radius=0.80m Speed=2.5m/s

Q: 4. (13.32) If 61.5 L of oxygen at 18.0°C and an absolute pressure of 2.45 atm are compressed to 38,8…

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

Q: If a 1.4 Volt battery is connected across point A and B, Find the ENERGY STORED in these network of…

Q: Which of the following is true? Passive elements are sources of electrical energy. Active elements…

A: Fifth option is correct

Q: Find the current Charge=600 C Time=60 s

A: Given data : Time=t Charge=Q To find : Current

Q: A 5.0 kg object has a momentum of 25.0 kg m/s west. What is its velocity? Show your work and…

A: Given data The mass of the object is given as m = 5 kg. The momentum of the object is given as P =…

Q: A 0.844 kg spring with force constant equal to 75 N/m oscillates with simple harmonic motion along…

Q: These are active devices that adapt the current they supply based on the load. Independent Current…

A: Third option is correct

Q: Given data: Distance to covered by car-22 m Time to cover the distance=2 s Find speed

A: Write the given values with the suitable variables. d=22 mt=2 s Here, d is the distance and t is the…

Q: Find work done Force=2 N Displacement=1.1 m

A: Given data : Force is demoted by F Displacement is denoted by d Required : Work done

Q: Find the man of object Density - 300 kg/m3 Valime = 0-2m³ 3

A: Given data : Density=ρ Volume=V Required : Mass

Q: Find the value of current Voltage=11 Volt Resistance-2 Ohm

Q: of a hemispherical dome at a velocity of 5 m/s. The diameter of the dome is 100 m. A searchlight was…

Q: Given data: Distance to covered by car-22 m Time to cover the distance-2 s Find speed

A: Given data : Distance = 22 m time taken to cover the distance = 2 s

Q: Question 15 In simple harmonic motion, the restoring force must be proportional to the: O…

A: Restoring force is defined as F = - k x where F = restoring force K = force constant x =…

Q: 5. The speed of transverse wave propagation on a tense string is 20 m/s when the tension is 100 N.…

Q: A hinged beam, 92.5 kg, is supported by a horizontal cable as in the figure. The length of the cable…

Q: 1. What is the pH of a solution prepared by mixing 80 ml of 0.1M NaH2PO4 and 100 ml of 0.1 M…

A: NaH2PO4 = weak acid = A =(80/1000)x0.1= 0.008 moles Na2HPO4 = conjugate base = B =…

Q: 7. The horizontal stick of length, L, shown in the figure is uniform and weighs 200 N. Calculate the…

A: Force brings about motion and changes in it. Free body diagram gives whole idea of the forces…

Q: If the charge inside a Gaussian surface is approximately 5.43x10^-6, and the flux is inward, how…

Q: 30 m Δ 40 m

A: Solution Correct option is (c)

Q: Find the value of kinetic energy mass of ball-2.2 kg Velocity=1.2 m/s

Q: Determine the electric current passing through each resistor in the following circuits. ww ++ R1 80…

Q: 2. A steel wire having cross-sectional area 1 mm' is stretched by 10 N. Find the lateral strain…

Q: The gap between electrodes in a spark plug is 0.060cm. Producing an electric spark in a gasoline-air…

A: Solution

Q: a) A coil with 50 turns of wire is wrapped around a tube with a cross-sectional area of 0.25 m^2. A…

Q: why u is equal to infinity?

A: As per rules of image formation, image should occur at focus, then object should be placed at very…

Q: 2. A neon sign emits electromagnetic radiation with a wavelength of 6.4 x10^-7 m . A) calculate the…

Q: When the amount of positive charges inside a box is doubled, which among the following is NOT a…

A: Introduction :- Here a positive charge is placed in box. We need to comment about the given four…

Q: The current is found to be 12.4mA when the metal is illuminated with a wavelength of 184.2nm. What…

Q: a) How many coils must a loop have with a cross-sectional area of 0.002 m^2 that is pulled through a…

Q: Directions: Write True if the statement is correct, and False if it is not. of light happens when…

A: 1) False - selective absorption happens. 2) False - visible light waves are the only EM waves we can…

Q: Problem 1: Light of frequency 9.95 x 1014 Hz ejects electrons from the surface of a metal. If the…

Q: Determine the reactions at A and B for the beams loaded as shown. Beam weight may be neglected. |50…

Q: 4.0kg object is moving across a friction-free surface with a constant velocity of 2ms–1. How much…

A: Given:- The mass of the object m = 4 kg The velocity of the object v = 2 m/s An object is moving…

Q: Let 2 vectors å anb b a 121=53161-5 in the plane of modules. How much is the magnitude of their e…

Q: Electric flux is inversely proportional to the surface area. To have a greater electric flux, one…

Q: What force keeps the pink and blue alien bttracted to the planet he is first sitting on?

A: Gravitational force

Q: What is the magnetic force that 0.75 m of a current-carrying wire experiences as 2.75 A of current…

A: The length of the current-carrying conductor, l = 0.75 m Current flowing through the conductor, i =…

Q: The SI unit for electric current is dimensionally equivalent to: ㅇ[c] [][] [c] - 1 [c][s] ㅇ[][c]

A: A stream of charged particles, such as electrons or ions, moving through an electrical conductor or…

Q: Explain what the rotating wave approximation means, and what justifies its use.

Question

Particle of mass m moves in a three-dimensional box with edge lengths L₁, L₂, and L₃.

(a) Find the energies of the six lowest states if L₁ =L, L₂ = 2L, and L₃ = 2L.

(b) Which if these energies are degenerate?

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

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

Similar questions

Show that the two lowest energy states of the simple harmonic oscillator, 0(x) and 1(x) from Equation 7.57, satisfy Equation 7.55. n(x)=Nne2x2/2Hn(x),n=0,1,2,3,.... h2md2(x)dx2+12m2x2(x)=E(x).
Suppose a wave function is discontinuous at some point. Can this function represent a quantum state of some physical particle? Why? Why not?
A 10 g marble is in a 1-D box of 10 cm. Assuming infinitely hard walls, (a) find its permitted energies (in J) and (b) the corresponding quantum number for the marble moving at 30 cm/s.
Seven electrons are trapped in a one-dimensional infinite potential well of width L.What multiple of h2/8mL2 gives the energy of the ground state of this system? Assume that the electrons do not interact with one another, and do not neglect spin.
The wave function for a quantum particle confined to moving in a one-dimensional box located between x = 0 and x = L is ψ(x) = A sin (nπx/L)Use the normalization condition on ψ to show that A = √2/L
If in a box with infinite walls of size 1 nm there is an electron in the energy state n=2, find its probability density, the wave function and the corresponding energy.
The normalised wavefunction for an electron in an infinite 1D potential well of length 89 pm can be written:ψ=(-0.696 ψ2)+(0.245 i ψ9)+(g ψ4). If the state is measured, there are three possible results (i.e. it is in the n=2, 9 or 4 state). What is the probability (in %) that it is in the n=4 state?
. Find the average (expectation) value of 1/r in the 1s state of hydrogen. Is the result equal to the inverse of the average value of r ? Note that the general expression is given by,
Three electrons are trapped in three different one-dimensional infinite potential wells of widths (a) 50 pm, (b) 200 pm, and (c) 100 pm. Rank the electrons according to their ground-state energies, greatest first.
What is the probability of finding a particle in the last 10% of a one-dimensional box for n = 1 state? Find the solution(s) to the differential equations: a. y''(x) + y'(x) - 6y(x) = 0 and b. y''(x) - 4y'(x) + 4y(x) = 0.
At what position is a particle in the second lowest energy state of a rigid box of length L most likely to be observed?
Consider a particle in 1D Box with length L, and in a state n = 4. What is the probability of finding the particle in the first 1/3 part of the box? exactly 1/4 exactly 1/6 less than 1/3 less than 1/4 none