## Question

###### Consider the harmonic oscillator wave function 1/4 where α = (-)"*. Here k, is the stiffness...

Consider the harmonic oscillator wave function 1/4 where α = (-)"*. Here k, is the stiffness coefficient of the oscillator and m is mass. Recall that the oscillation frequency iso,s:,k, / m In class we showed that Ψ0(x) Is an eigenfunction of the Hamiltonian, with an eigenvalue Eo (1/2)ha a) Normalize the wave function in Eq.(1) b) Graph the probability density. Note that a has units of length and measures the "width" of the wave function. It's easier to use x/a in labeling the x-axis. c) Calculate the uncertainty in x. Ar=kr>-<i> . Leave your answers in terms o d) Calculate the uncertainty in p, Ap= p>-<p> e) Show that the uncertainty principle is satisfied. , -ba 2b Hints. (16x dx = π / b x e ax 2b

## Answers

Psi_0 (x) = N e -x^2/2 alpha^2 Now Normalization integral^infinity_- infinity psi*_0 (x) pai_0 (x) dx = 1 Because N^2 integral^infinity_-infinity -x^2/alpha^2 dx = 1 Here b = 1/alpha^2 [integral^infinity_-infinity e^bx^2 dx = squareroot pi/b] because N^2 squareroot pi/(1/alpha)^2 = 1 N = 1/squareroot alpha^2 pi = > N = 1/alpha squareroot pi probability DensityVertical-bar psi* (x) psi (x) Vertical-bar = N^2 e^-x^2/alpha^2Vertical-bar psi Vertical-bar ^2 = 1/alpha^2 pi e^-x^2/alpha^2 \r\n delta x = squareroot < x^A2 > - < x > ^2 Because < x > = integral^infinity_-infinity psi* (x) x psi (x) dx/integral^infinity_infinity Vertical-bar psi Vertical-bar ^2 dx = N^2 integral^infinity_-infinity xe^-x^2/alpha^2 dx/1 < x > = 1/alpha^2 pi integral^infinity_-infinity k e^-x^2/alpha^2 dx using integral^infinity_-infinity x^2 b^-bx^2 dx = squareroot pi/b/2b Here b = 1/alpha^2 < x^2 > = 1/alpha^2 pi . squareroot pi (1/alpha^2)/2 (1/alpha^2) < x^2 > = 1/2pi squareroot alpha^2 pi = > < x^2 > = alpha/2 squareroot pi using (2) & (3) delta x = squareroot < x^2 > - < x > ^2 delta x = (alpha/2 squareroot pi)^1/2 \r\n {p^^ > = integral^infinity_-infinity psi* (x) (-ihd/dx) psi (x) dx = -ih/alpha^2 pi integral^infinity_-infinity e^-x^2/2 alpha^2

#### Similar Solved Questions

1 answers

##### PPE is usually low risk because of the number of transactions involved. Do you (dis)agree with...

PPE is usually low risk because of the number of transactions involved. Do you (dis)agree with the statement and why?...

4 answers

##### For a particular game, 10 balls are selected at random from 80 balls numbered 1-80. Use...

For a particular game, 10 balls are selected at random from 80 balls numbered 1-80. Use the included table of random numbers to simulate one game by obtaining 10 random numbers between 1 and 80. Start at the two-digit number in line number 3 and column numbers 13-14, read down the column, up the nex...

1 answers

##### How do you evaluate #e^( ( 13 pi)/8 i) - e^( ( pi)/4 i)# using trigonometric functions?

How do you evaluate #e^( ( 13 pi)/8 i) - e^( ( pi)/4 i)# using trigonometric functions?...

1 answers

##### How do you combine like terms in #5t + 8d - 2t - 3d#?

How do you combine like terms in #5t + 8d - 2t - 3d#?...

1 answers

##### QUESTION 9 What is the map distance between lys and val? Tetrad A Tetrad B Tetrad...

QUESTION 9 What is the map distance between lys and val? Tetrad A Tetrad B Tetrad Tetrad D Tetrad e Tetrad F lys + lys + lys val lys val lys val + val lys + lys val lys val lys + + val lys + + val + + + + + + lys + + val + val + val + + + val + + lys + | 36 12 376 81 + + + + + +1 OOOO 13.5 the loci ...

1 answers

##### A circular loop of wire with area A lies in the y-plane. As viewed along the...

A circular loop of wire with area A lies in the y-plane. As viewed along the z axis looking in the -z direction toward the origin, a current I is circulating clockwise around the loop. The torque produced by an external magnetic field B is given by tau = D(4i - 4j), where D is a positive constant, a...

1 answers

##### Om anyone) • Time Limit: 170 minutes (2 hours and 50 minutes) Question 18 3 pts...

om anyone) • Time Limit: 170 minutes (2 hours and 50 minutes) Question 18 3 pts A pickup truck has a width of 61.7 in. If it is traveling north at 32 m/s through a magnetic field with vertical component of 36 mT, what magnitude emfis induced between the driver and passenger sides of the truck 0...

1 answers

##### Question 1 A crane is used to lower weights into a lake for an underwater construction...

Question 1 A crane is used to lower weights into a lake for an underwater construction project. Determine the tension in the rope of the crane due to a Im-diameter spherical steel block (density 88.005 g/cm²) when it is (a) suspended in the air and (b) completely immersed in water....

1 answers

##### Researchers wanted to study if havinga long beak is related to flight in birds. They surveyed...

Researchers wanted to study if havinga long beak is related to flight in birds. They surveyed a total of 34 birds. The data are shown in the contingency table below. What is the relative risk of having long beaks for those birds that fly? Round your answer to two decimal places. Flies Does not fly T...

1 answers

##### Comparative financial statements for Weaver Company follow: Weaver Company Comparative Balance Sheet at December 31 This...

Comparative financial statements for Weaver Company follow: Weaver Company Comparative Balance Sheet at December 31 This Year Last Year $ $ 13 670 30 410 -Book 255 prences Assets Cash and cash equivalents Accounts receivable Inventory Prepaid expenses Total current assets Property, plant, and equipm...

1 answers

##### Classifying Balance Sheet and Income Statement Accounts and Computing Current Ratio Shoprite Holdings Ltd is an...

Classifying Balance Sheet and Income Statement Accounts and Computing Current Ratio Shoprite Holdings Ltd is an African food retailer listed on the Johannesburg Stock Exchange. The following accounts are selected from its annual report for the fiscal year ended June 30, 2014. The amounts below are i...

1 answers

##### Year Project Al-$5,000 $0 $2,000 $4,000 $6,000 $8,000 Project B -$10,000 SO $0 $8,000 $16,000 $16,000...

Year Project Al-$5,000 $0 $2,000 $4,000 $6,000 $8,000 Project B -$10,000 SO $0 $8,000 $16,000 $16,000 Project C-$20,000-$5,000 $0 $0 $0 $60,000 Assume an interest rate of 9%, what project should be chosen? What about 12%? You should assume compound interest...

1 answers

##### Provide an appropriate response. The cholesterol levels (in milligrams per deciliter) of 30 adults are listed...

Provide an appropriate response. The cholesterol levels (in milligrams per deciliter) of 30 adults are listed below. Find the percentile that corresponds to a cholesterol level of 238 milligrams per deciliter. 154 156 165 165 170 171 172 180 184 155 189 189 190 192 195 198 199 200 200 200 205 205 21...

1 answers

##### Write out the general equation representing anaerobic alcoholic fermentation of glucose.

Write out the general equation representing anaerobic alcoholic fermentation of glucose....

1 answers

##### Help please Water flows at 150 ft3 /s down a rectangular channel made of finished concrete....

help please Water flows at 150 ft3 /s down a rectangular channel made of finished concrete. The channel has a width of 10 ft and a downward slope of 0.0002, and the water depth is 4 ft at the control section A. (Figure 1) Part A Determine the distance z from A to where the depth becomes 3.5 ft. Take...

1 answers

##### 2) Draw a reaction coordinate diagram for the following reaction. Be sure to label any transition states or intermed...

2) Draw a reaction coordinate diagram for the following reaction. Be sure to label any transition states or intermediates. (4 points) NaSH SH...

1 answers

##### What elements does the array numbers contain after the following code is executec int[] numbers =...

What elements does the array numbers contain after the following code is executec int[] numbers = new int [8]; numbers [1] = 3; numbers [4] = 99; numbers [7] = 2; int x = numbers[1]; numbers(x) = 44; numbers (numbers [7]] = 11; O 13, 11, 44, 99, 2] O 10, 3, 11, 44, 99, 0, 0, 2] O 13, 0, 11, 44, 99, ...

1 answers

##### An 80.0 kg bungee jumper drops from rest off a bridge that is 200.0 m above...

An 80.0 kg bungee jumper drops from rest off a bridge that is 200.0 m above a river. As he falls, air resistance is negligible, and the unstretched bungee cord attached to him uncoils. The mass of the bungee cord is negligible. When the jumper is 50.0 m below the bridge, the bungee cord is completel...