Take as a a trial function for the ground state of the hydrogen atom (a) e^(−kr),...
Take as a a trial function for the ground state of the hydrogen atom (a) e^(−kr), (b) e^(−kr^2) and use the variational principle to find the optimal value of k in each case. Identify the better wavefunction. The only part of the laplacian that need be considered is the part that involves radial derivatives.
Please show your work and explain your answer so I can follow along
yes it's not organic chemistry, its quantum mechanics (chemistry)
Homework Answers
Add Answer to:
Take as a a trial function for the ground state of the hydrogen
atom (a) e^(−kr),...
45. Use a Gaussian trial function o(r) = e" to compute the ground state energy of...
45. Use a Gaussian trial function o(r) = e" to compute the ground state energy of the hydrogen atom. What is the "best" value of the variational parameter a? How far off is this energy from the true value?
1) (60 points) The ground state of the hydrogen atom: In three dimensions, the radial part...
1) (60 points) The ground state of the hydrogen atom: In three dimensions, the radial part of the Schrodinger equation appropriate for the ground state of the hydrogen atom is given by: ke2 -ħ2 d2 (rR) = E(rR) 2me dr2 where R(r) is a function of r. Here, since we have no angular momentum in the ground state the angular-momentum quantum number /=0. (a) Show that the function R(r) = Ae-Br satisfies the radial Schrodinger equation, and determine the values...
(VI) Hydrogen atom A What is the probability that an electron in the ground state of...
(VI) Hydrogen atom A What is the probability that an electron in the ground state of hydrogen will be found inside the nucleus? Find the expression for the probability, in which Rc denotes the the radius of nucleus. Hints: Rc IT 127 i) Integration in spherical coordinate system (r, 0, 0)|r2 sin Ododedr Jo Jo Jo 2.c 20 e Jo a 2 B Construct the wavefunction for an electron in the state defined by the three quantum numbers: principal n...
In this optional assignment you will find the eigenfunctions and eigenenergies of the hydrogen atom using an operator method which involves using Supersymmetric Quantum Mechanics (SUSY QM). In t...
In this optional assignment you will find the eigenfunctions and eigenenergies of the hydrogen atom using an operator method which involves using Supersymmetric Quantum Mechanics (SUSY QM). In the SUSY QM formalism, any smooth potential Vx) (or equivalently Vr)) can be rewritten in terms of a superpotential Wix)l (Based upon lecture notes for 8.05 Quantum Krishna Rajagopal at MIT Physics II as taught by Prof Recall that the Schroedinger radial equation for the radial wavefunction u(r)-r Rfr) can be rewritten...
Tl 6. (4 pts) We calculated Ahf for the ground state Hydrogen atom, but now let us consider Hht f...
Tl 6. (4 pts) We calculated Ahf for the ground state Hydrogen atom, but now let us consider Hht for the ground state of the deuterium atom. The basic idea is the same: Here the matrix representation of S is the same, since it represents the spin operator for the spin- electron, but that of 7 is different because the deuteron is a spin-1 particle (neutron+proton) whose spin has 3 possible values for the magnetic quantum number. Also, we must...
45. Use a Gaussian trial function o(r) = e" to compute the ground state energy of the hydrogen atom. What is the "best" value of the variational parameter a? How far off is this energy from the true value?
1) (60 points) The ground state of the hydrogen atom: In three dimensions, the radial part of the Schrodinger equation appropriate for the ground state of the hydrogen atom is given by: ke2 -ħ2 d2 (rR) = E(rR) 2me dr2 where R(r) is a function of r. Here, since we have no angular momentum in the ground state the angular-momentum quantum number /=0. (a) Show that the function R(r) = Ae-Br satisfies the radial Schrodinger equation, and determine the values...
(VI) Hydrogen atom A What is the probability that an electron in the ground state of hydrogen will be found inside the nucleus? Find the expression for the probability, in which Rc denotes the the radius of nucleus. Hints: Rc IT 127 i) Integration in spherical coordinate system (r, 0, 0)|r2 sin Ododedr Jo Jo Jo 2.c 20 e Jo a 2 B Construct the wavefunction for an electron in the state defined by the three quantum numbers: principal n...
In this optional assignment you will find the eigenfunctions and eigenenergies of the hydrogen atom using an operator method which involves using Supersymmetric Quantum Mechanics (SUSY QM). In the SUSY QM formalism, any smooth potential Vx) (or equivalently Vr)) can be rewritten in terms of a superpotential Wix)l (Based upon lecture notes for 8.05 Quantum Krishna Rajagopal at MIT Physics II as taught by Prof Recall that the Schroedinger radial equation for the radial wavefunction u(r)-r Rfr) can be rewritten...
Tl 6. (4 pts) We calculated Ahf for the ground state Hydrogen atom, but now let us consider Hht for the ground state of the deuterium atom. The basic idea is the same: Here the matrix representation of S is the same, since it represents the spin operator for the spin- electron, but that of 7 is different because the deuteron is a spin-1 particle (neutron+proton) whose spin has 3 possible values for the magnetic quantum number. Also, we must...
Most questions answered within 3 hours.
-
An interest rate swap has three years of remaining life.
Payments are exchanged annually. Interest at...
asked 4 seconds ago -
there are many issues that can be addressed when performing a
RCA. Assuming that there is...
asked 1 minute from now -
ata pertaining to the postretirement health care benefit plan of
Danielson Delivery Service include the following...
asked 38 seconds ago -
Getting along with the members of your team requires good ____
skills.
a.
authoritative
b.
problem...
asked 8 minutes ago -
During June, Propene Company produced 20,000 chainsaw blades.
The standard quantity of material allowed per unit...
asked 14 minutes ago -
Draw the molecular orbital energy level diagrams and write the
electron configurations of (a) Be2, (b)...
asked 14 minutes ago -
We put a mixture of helium, oxygen and nitrogen gases in a
closed container at 25...
asked 24 minutes ago -
You measure 22 dogs' weights, and find they have a mean weight
of 64 ounces. Assume...
asked 32 minutes ago -
Complete and balance the following methesis reaction in aqueous
solution.
Instructions
• Use proper element capitalization....
asked 44 minutes ago -
Green Tree Corporation is expecting to receive $0.5 million at
the end of Year 1, $0.25...
asked 52 minutes ago -
A face value of $10,000 is assumed for these Treasury bills.
Maturity Days to Maturity Bank...
asked 48 minutes ago -
Please read the article attached.Under Armour Is Subject of
Federal Accounting Probes - WSJ.pdf Under Armour,...
asked 46 minutes ago