The Hamiltonian operator for a one-dimensional harmonic oscillator moving in the x direction is Find the value
Question:
Find the value of the constant a such that the function eax2 is an eigenfunction of the Hamiltonian operator and find the eigenvalue E. The quantity k is the force constant, m is the mass of the oscillating panicle, and is Plancks constant divided by 2Ï.
h? d? kx? Н- 2m dx2 2
Step by Step Answer:
Divide by e ax2 The coefficients of x 2 on the two sides o...View the full answer
Related Video
In Physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity, i.e., to accelerate. Force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity. In this video, the concept of force and torque is demonstrated with the practical application of changing the flat tire of the car.
Students also viewed these Mathematics questions
-
Find the eigenfunction of the Hamiltonian operator for motion in the x direction if V(x) = E 0 = constant.
-
Changing Frequencies Consider the undamped harmonic oscillator defined by + (20x = 0 with initial conditions x(0) = 4 and (0) = 0. (a) For (0 = 0.5, I, and 2, the corresponding trajectories are...
-
According to quantum mechanics, the energy of a harmonic oscillator is quantized. That is, it can take on any one of a certain set of values, given by where h is Plancks constant, equal to 6.62608...
-
Draw structures for the following molecules (a) Acrylonitrile, C3H3N, which contains a carbon-carbon double bond and a carbon-nitrogen triple bond (b) Ethyl methyl ether, C3H8O, which contains an...
-
Journalize, record, and post when appropriate the following transactions in the general journal (all sales carry terms of 5/10, n/30): 201X Aug. 16 Sold merchandise on account to Ralph Co., invoice...
-
Problem 5 Lily provided the following data to you for taxable year 2023: Net Sales Cost of Goods Sold P19,000,000.00 P4,600,000.00 Other Non-Operating Income Ordinary and Actual Business Expenses VAT...
-
The Chernobyl disaster was a catastrophic nuclear accident that occurred on April 26, 1986, at the Chernobyl Nuclear Power Plant in Ukraine, which was under the direct jurisdiction of the central...
-
J. Ortiz Wholesale Corp. uses the LIFO method of inventory costing. In the current year, profit at B. J. Ortiz is running unusually high. The corporate tax rate is also high this year, but it is...
-
What is the Profit maximizing product level and why? What is the Profit maximizing price and why? *This is for Q4, the 50 and $60 is incorrect Total Profits/ Price Output TR MR TC TFC TVC AFC AVC ATC...
-
Farris Casinos recently acquired a newly built hotel and casino in Atlantic City. The cost of the complex was $ 6,000,000, with a six- year useful life and no residual value expected. Farris...
-
In quantum mechanics, the expectation value of a mechanical quantity is given by where AÌ is the operator for the mechanical quantity and Ï is the wave function for the state of the...
-
The components of the angular momentum correspond to the quantum-mechanical operators: These operators do not commute with each other. Find the commutator [LÌ x , LÌ y ]. x y y- i z...
-
The article Checks Halt over 200,000 Gun Sales (San Luis Obispo Tribune, June 5, 2000) reported that required background checks blocked 204,000 gun sales in 1999. The article also indicated that...
-
If 12,500TL is invested in compound interest at 20% per annum, what will be its value at the end of the second year? (5 POINTS)Our formula Sa (1 + 1)n
-
What would be the answer if the life expectancy is 95 instead of 101. What would be the answer of this assignment under the assumption- Zero current savings, no tax implications, 1% Management Fee...
-
asks how much the brokerage commission is in connection with the sale (Exhibit 7-4), and who is responsible for paying it?
-
Perform a SWOT analysis for your simulation firm. List several items in each category. Identify your firm's strategy as either low-cost or differentiation. If you have different strategies for the AC...
-
Suppose that Penny Chairs has three media options: radio, TV, and ads in Furniture World (an industry publication). The table below provides information related to the costs, exposure values (i.e....
-
Given H = (3r 2 / sin )a + 54r cos a A/m in free space: (a) Find the total current in the a direction through the conical surface = 20, 0 2, 0 r 5, by whatever side of Stokes theorem you...
-
Rosalie owns 50% of the outstanding stock of Salmon Corporation. In a qualifying stock redemption, Salmon distributes $80,000 to Rosalie in exchange for one-half of her shares, which have a basis of...
-
Implement the test in Problem 9.47, and report a two-tailed p-value?
-
Implement the test in Problem 9.47, and report a twotailed p-value? Table 9.15: (Weight change, control period) (weight change, lack-of-consistency period) among 23 adolescent diabetic boys 4, A....
-
Answer the question in Problem 9.45 if we are not willing to make the assumption of normality? Table 9.15: (Weight change, control period) (weight change, lack-of-consistency period) among 23...
-
Find f'(x) and find the equation of the line tangent to the graph of f at x = 1. f(x)=(1+4x)(5-4x) f'(x)=
-
Find f'(x) and find the equation of the line tangent to the graph of f at x = 3. f(x)= 5x 2* f'(x)=
-
A bacteria culture starts with 340 bacteria and grows at a rate proportional to its size. After 2 hours there will be 680 bacteria. (a) Express the population P after t hours as a function of t. Be...
Study smarter with the SolutionInn App