Answered: Example 5. The Hamiltonian of a system… | bartleby

Related questions

Question

Example 5. The Hamiltonian of a system is given by
-n? d?
2m d2 a6 (x)
where 'a' is a constant and & (x) is Dirac's delta function. Estimate the ground state energy ofthe system
%3D
using a Gaussian trial function.

Expert Solution

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

1- by using the Covariance theory to find the wave function of a harmonic oscillator, we use the following function : A x2 + b Where A is a normalize constant and b is Covariance coefficient . a- Calculate the Normalize constant A ( the given : 1 dx ) 2byb h? 1 b- if the Hamiltonian calculation gives a value of ( (H) mw²b + ) 2m b determine the ground energy value of the harmonic oscillator
Q1 For a simple harmonic oscillator particle exist up to the second excited state (n-2). N what is the matrix representation for the linear momentum. Take The Ladder operators properties, where la,n) = vn +1m+ 1), andja_n) = nvn- 1) %3D !3! 1 %3D (P t imwx) Vzm Where
A11
Question A6 Consider an infinite square well with V = 0 in the interval -L/2 < x < L/2, and V → ∞ everywhere else. A particle of mass m is in the groundstate of this system, and is known to have a wavefunction and energy given by TX √ = COS and E = π²h² 2mL² The system is then perturbed so that its potential takes the constant value V
Can you elaborate on the dirac notation for the raising and lowering operators. I am not understanding how you got (6n^2+6n+3)
6
You are given a free particle (no potential) Hamiltonian Ĥ dependent wave-functions = -it 2h7² m sin(2x) e = V₁(x, t) V₂(x, t) 2 sin(x)e -ithm + sin(2x)e¯ What would be results of kinetic energy measurements for these two wave-functions? Give only possible outcomes, for example, it is possible to get the following values 5, 6, and 7. No need to provide corresponding probabilities. ħ² d² 2m dx2 and two time- -it 2hr 2 m
6. In Dirac notation, after the equation Bø) = b|p)is solved, we often write the solutions as {|Øn)} and {bn}. The name given to {b,} is it is the spectrum of the operator B . Essentially problem 5 and problem 6 are describing identical situations. What is the relationship between pn (x) and |Øn)? To answer this, give a mathematical answer and a physical interpretation of what it means. Hint: If you do not know how to answer this off the top of your head as being obvious, review my notes on Dirac notation and how vectors are used in quantum mechanics.
A) Explain what the difference is between the “center of mass” and the “centroid” of an object. B) how is moment of inertia related to kinetic energy? C) Explain what a joint probability density function is supposed to measure.
Q2 (a) An oscillator consisting of a mass of 1g on a spring exhibits a period of 1 s. The velocity of the mass when it crosses the zero displacement position id 10 cm/s. (i) Is the oscillator possibly in an eigenstate of the Hamiltonian ? (ii) Find the approximate value of the quantum number n associated with the energy E of the oscillator. (iii) Has the zero point energy any significance here?
The potential for an anharmonic oscillator is U = kx²/2 + bx*/4 where k and b are constants. Find Hamilton's equations of motion. %3D
Question A2 Consider an infinite square well of width L, with V = 0 in the region -L/2 < x < L/2 and V → ∞ everywhere else. For this system: a) Write down and solve the time-independent Schrödinger equation for & inside the well, where -L/2< x

SEE MORE QUESTIONS