2. Variational Principle. The energy of a system with wave function ψ is given by where...

Question:

2. Variational Principle. The energy of a system with wave function ψ is given by where H is the energy operator. The variational principle is a method by which we guess a trial form for the wave function φ, with adjustable parameters, and minimize the resulting energy with respect to the adjustable parameters. This essentially chooses a "best fit" wave function based on our guess. Since the energy of the system with the correct wave function will always be minimum our guess will always lead to an energy which is slightly too high, but the variational principle allows us to get as close as possible to the correct energy with our trial wave function Use the variational principle to estimate the ground state energy for the anharmonic oscillator, 2m 2 Compare your result with the exact result 1m Note that this is a one-dimensional problem, so take dV-dx. You know physically that a trial function must be peaked around x-0 and must be normalizable (i.e.. Jo o ψ2ax is finite). Such functions would include e-e or 1/(c +x2), or the harmonic oscillator ground state wave function for instance. Choose wisely, and the mathematics will be far simpler.

Similar Solved Questions

Question 10 (0 points) 0.5 07 Examine the nonlinear function displayed above. Consider the range bounded...
Question 10 (0 points) 0.5 07 Examine the nonlinear function displayed above. Consider the range bounded by -2 < X < +2 and -2 <Y < +2. Check all of the statements that are true. (There may be more than one true statement.) -2 < X < +2 and -2 < Y < +2. Check all of the statem...
Given the following, determine the maximum, minimum, and x-intercepts in the interval [-2p,2p]....
Given the following, determine the maximum, minimum, and x-intercepts in the interval [-2p,2p].y=3cos(x/2)...
How much force is needed to accelerate a 4.0 kg physics book to an acceleration of 2.0 m/s^2?
How much force is needed to accelerate a 4.0 kg physics book to an acceleration of 2.0 m/s^2?...
Find the point of intersection of the line 1) Find the equation of the line passing...
find the point of intersection of the line 1) Find the equation of the line passing through the points A(1,-5,-3)and B(2,-4,8) (3 marks) b) Find the equation of the plane perpendicular to the line in part (a) given that C(1,-9,6) is a point on the plane. (3 marks) c) Find the point of intersecti...
Activity Rates Zapato Company produces two types of boots: vaquero and vaquera. There are four activities...
Activity Rates Zapato Company produces two types of boots: vaquero and vaquera. There are four activities associated with the two products. Drivers for the four activities are as follows: Vaquero 2,400 2,850 650 Vaquera 5,400 4,650 Cutting hours Assembly hours Inspection hours Rework hours 2,430 The...
Propose a synthesis for the following conversion. It will take more than one step. Show the...
Propose a synthesis for the following conversion. It will take more than one step. Show the product of each reaction you propose to use. [6 points] CN...
Madison Park Co-op, a whole foods grocery and gift shop, has provided the following data to...
Madison Park Co-op, a whole foods grocery and gift shop, has provided the following data to be used in its service department cost allocations: Departmental costs before allocations Employee-hours Space occupied-square feet Service Departments Administration Janitorial $190,000$60,000 460 330 900 1...
A circle's center is at (8 ,7 ) and it passes through (6 ,5 ). What is the length of an arc covering (5 pi ) /6  radians on the circle?
A circle's center is at (8 ,7 ) and it passes through (6 ,5 ). What is the length of an arc covering (5 pi ) /6  radians on the circle?...