Derive Schrodinger equation? Write its application to particle in one dimensional x. Also prove that this a Eigen value problem.

Q: Consider an electron in the hydrogen atom. The electron is initially in the groundstate. a) If…

A:

Q: Convince yourself that function exp(-x2/2) is an eigenfunction of the operator (1/2)(-d2/dx2 + x2).…

A:

Q: al box oscillator

A: Zero point energy is a lowest energy ( ground state ) in 1D box and harmonic oscillator and Hydrogen…

Q: How many different configurations can I form with 4 electrons and 6 orbitals (i.e. spatial…

A: Microstates or number of ways = N!n! × (N-n)!

Q: Give a clear handwritten answer with explanation..give only handwritten answer Which characteristics…

A: The two quantum chemical calculations must have the same basis set and the same level of theory.…

Q: It is given the electronic orbit of atom A with a circumference of 2.5 times the wavelength de…

A: The wave properties of matter or the wave nature of an electron is given by de Broglie equation: λ =…

Q: Draw the first three functions of the particle in the box at a distance of 0 to a

A:

Q: ) Confirm that the wavefunction for the first excited state (v = 1) of a quantum harmo scillator is…

A:

Q: Schrödinger equation for a hydrogen atom. (i) State the Hamiltonian operator for a hydrogen atom.…

A:

Q: * 14) For the same He, write out the ground state wavefunction. (you can leave it in the form of…

A:

Q: 3. Show that for the 1-D particle-in-a-box, Y₁ is orthogonal to Y2.

A: The objective of the question is to demonstrate that the wavefunctions Y1 and Y2 of a…

Q: Which of the following functions are eigenfunctions of the operator ·Â if  = d² f(x)/dx²? Check all…

A:

Q: Use the appropriate Hamiltonian operator and eigen function to calculate the eigenvalue for a…

A:

Q: Prove that two eigenfunctions of a Hermitian operator that corresponds to two different eigenvalues…

A: Quantum chemistry is a branch of physical chemistry that based on the application of quantum…

Q: onsider the free-particle Schrodinger equation in three dimensions and electrons are confined to a…

A: SOLUTION: Step 1: The relation between the magnitude of the wave factor (k) and the energy at the…

Q: The Hückel determinant for a 4 Carbon containing conjugated cyclic molecule has four roots…

A:

Q: Without solving any integrals, calculate the average potential energy and average kinetic energy (in…

A:

Q: Problem What values of the angular momentum (l ) and magnetic (ml) quantum numbers are allowed for a…

A: The principal quantum number was introduced by Neils Bohr. It was represented by n.  The azimuthal…

Q: Consider the localized wavefunction given by ul x) = e-x?/2. Use the definitions = x d and match the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Please answer this problem in handwritting, NOT TYPED!!!

A:

Q: a. Write out all the kinetic and potential energy terms for the energy operator for the neutral Li…

A: Quantum mechanics revolutionized our understanding of the microscopic world, providing a robust…

Q: Do the total energy and the momentum operators commute? If yes, determine the eigenvalue. If not,…

A: To predict whether the total energy and the momentum operators commute or not.

Q: occurrence

A:

Q: show that ψ2 and ψ3 for the harmonic oscillator are orthogonal

A:

Q: which quantum number is not derived from the solution of Schrodinger wave equation for hydrogen…

A: Spin quantum number (ms)  is not derived from the solution of schrodinger wave equation for hydrogen…

Q: In quantum mechanics, a physically acceptable wave function must be what? a. Have imaginary…

A: An acceptable wave function ia that whose solutions are real and it must be single valued(one value…

Q: Effect of De Broglie wave particle duality and Heisenberg uncertainty principle these tow phenomena…

A: Electromagnetic spectrum involves different radiations from the lowest to the highest frequency…

Q: Derive and explain the results of Hydrogen atom in Quantum mechanics by applying schrodinger…

A: A mathematical equation that is being used in determining the position and energy of the electron in…

Q: Are the following eigenfunctions of the inversion operator, i, which has the effect of replacing x…

A: Eigen function and eigen value

Q: None

A: d) A function that preserves limits of sequences. a) A function that can be expressed as a ratio of…

Q: 1. Please write out a possible Slater Determinant for the ground state of lithium atom?

A: The objective of the question is to write the Slater Determinant for the ground state of lithium.

Q: In order to solve the TISEq for the water molecule we need to first invoke an important…

A: The approximation needed to solve the time independent Schrodinger wave equation for water molecule.

Q: Write and evaluate the slater determinant for Li atom. Provide clear handwriting and clear image

A: Slater determinants are constructed by arranging spinorbitals in columns and electron labels in rows…

Q: 1.13 A one-particle, one-dimensional system has the state function = (sin ar) (2/mc²)¹/4²³1²³² +…

A: A particle in a 1-dimensional box is a fundamental quantum mechanical approximation describing the…

Q: Calculate the probability of finding an electron in a 1s orbital outside the Bohr orbit (ao). Show…

A: Radial distribution function is given by,

Q: The simplest guess wave function for H2* has two coefficients, c1 and c2. How big would be the…

A: If the equation have two coefficient c1 & C2 . Then in secular equation the matrix will be…

Q: The angular momentum quantum number can be negative or positive. True False

A: Angular Momentum Quantum number tells us about the shape of orbitals ( subshells ) s,p d and f .

Q: 2. Show that the set of one-dimensional particle in the box functions where n = 1,2,3... are…

A: The proof is given as follows:

Q: 7. Consider the eigenfunction below: Wave Function

A: Find the average kinetic energy and the average potential energy of a particle in the ground state…

Q: 1. Show that wavefunctions in particle in a box are orthonormal

A:

Q: Suppose a hydrogen atom state was approximated by the function 1s + 2s + 3s where 1s, 2s and 3s are…

A: Solution is in next step

Q: Consider the follow image of two waves (i.e., orange and black oscillatory curves). Note that the…

A: A question based on general chemistry that is to be accomplished.

Q: [4] Write down an expression for the average potential energy of a harmonic ocillator in the first…

A: This is how we can calculate

Quantum Chemistry

Quantum chemistry deals with the properties of chemical systems and their reactions. The branch of chemistry which is more concerned with quantum chemistry is physical chemistry. It is a more sophisticated field of theoretical physics which is concerned towards the application of physical concepts towards various chemical aspects such as, formation of atoms, chemical structure descriptions, chemical bond strength, hybridization, conjugation etc. Quantum chemistry mainly studies the various states i.e., ground state, excited state, transition states of the individual atoms or molecules taking place during any chemical reaction. The laws of motion explained by various scientists, which are termed as “classical mechanics” were not acceptable in terms of electrons, protons, atoms, light etc. Thus, a new theory named “quantum mechanics” emerged to understand the basic framework of various atomic and subatomic particles.