Q6. Prove that wl and y3 of particle in one-dimensional-box are orthonormal

Q: Suppose that particle in two-dimensional (2D) box a a x; 30 V(xy) = x(а — х) у(b-у) (a³b5)i] Show…

A: We have the following two  points from the question: The particle is in a 2D box The wave function…

Q: hat are the functions of the salt bridge? a. Explain in point form all p

A: Given What are the functions of the salt bridge?a. Explain in point form all possibilities

Q: Sketch the boundary surface of a dx2 −y2 and a py orbital. Be sure to show and label the axes.

A: The shapes of different orbital are as follows: The shape of s-orbital is sphere. The shape of…

Q: What is the degeneracy of a molecule rotating with J = 4?

A: Degeneracy of energy levels- Simple meaning of degeneracy of energy levels is energy levels with…

Q: onstruct a slater determinant for the ground state He atom and show that is gives you, Ψ=1s α(2)1s…

A: In quantum mechanics, a slater determinant determines the asymmetric wave function for a…

Q: This problem illustrates the application of Linear Variational Theory. Consider a particle of mass m…

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Q: Sketch the form of the wavefunctions for the harmonic oscillator with quantum numbers v = 0 and 1.…

A: Harmonic oscillator explains vibrational motion of particle. In quantum mechanical model, the…

Q: Write out the 3x3 matrices for the C, G, and a transformations operating upon the vector (x, y, z).…

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

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Q: 1) energy levels. In particular, sketch the wavefunctions that correspond to the lowest 4 energy…

A: As energy levels increses the energy gap between levels increases.

Q: Consider the real part of the spherical harmonic Y2,+2. At which values of ϕ do angular nodes occur?…

A: The spherical harmonic Y2+2, is given below. The number of angular nodes is given by the formula…

Q: For a particle in a rectangular box with sides of length L1 = L and L2 = 2L, find a state that is…

A: Degenerate state is that when two or more than two states of quantum system gives same value of…

Q: Confirm that the kinetic energy operator, −(ħ2/2m)d2/dx2, is hermitian.

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Q: What is the degeneracy of a molecule rotating with J = 3?

A: The phenomenon by which a single energy level corresponds to two or more than two states of motion…

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

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Q: Sketch the form of the wavefunctions for the harmonic oscillator with quantum numbers v = 1 and 2.…

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Q: What is the dissociation energy, D (in kJ/mole) for this Morse oscillator?

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

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Q: How many nodes are there in the p LUMO wavefunction of 1,3,5-hexatriene? Answer with ONLY an…

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Q: Q4: Derive planar density expressions for BCC (100) and (110) planes in terms of the atomic radius…

A: (1,0,0) plane within a BCC unit cell si given below.

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

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Q: y-projection of the spin operator sy = e eigen values and the normalized eigen fun the eigen…

A: Given: Sy=h20-ii0=0-ih2ih20

Q: the above are correct Q8) If the operator A acts on the orthonormalized real functions f; and f; as…

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Q: What is the eigen value when the eigen function e* is operated on the operator d" I dx" ? ( A ) α"…

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Q: Determine the ground-state terms for the d and d configurations and their degeneracies.

A: To determine:  ground state terms for d3 and d6  their degeneracy = ?

Q: What is the eigen value of the function e* when operated on the operator d" / dx" ? (A) a" (В) ха"…

A: The Hermitian equation is shown below: A^ψ=aψ where; a = eigen value A^ = operator ψ = eigen…

Q: B A D +y -IN -IM

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Q: c. A real system is the vanadium atom with the following electronic energy level scheme: Level…

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Q: how many terms are there in the total Hamiltonian of the hydrogen molecule?

A: In quantum, the hamiltonian operator corresponds to the total energy of the system. The total energy…

Q: Solve the both questions

A: Q.1. The given wave function is- ψ(x) = coskx Hx^=-h22m∂2∂x2+Vx Now, to check for Eigenfunction it…

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: e) Prove that it is impossible to construct a completely antisymmetric spin function for three…

A: Consider three or any number bigger than 2 electrons without spatial degrees of freedom,thus the…

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

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Q: el Write out the 3x3 matrices for the C, G and o transformations operating upon the vector (x, y,…

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Q: Show that all three sigma v operations in the group D3h belong to the same class.

A: A Point Group tells about all the symmetry operations that can be performed on a molecule.

Q: Prove

A: He2 have total number of electrons is equal to 2 • 2 = 4 electron ( each He atom have 2 electrons )…

Q: What is the eigen value when the eigen function eª* is operated on the operator d" / dx" ? (А) а "…

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Q: If the operator A acts on the orthonormalized real functions f, and f₂ as Af₁ = f₂ and Âf₂ = f₁. The…

A: Here we are required to find the expectation value.Given

Q: Q18. What is the degeneracy of a state Wizs for a particle confined in cubic box? F) 5 B) 3 C) 4 D)…

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Q: Confirm that the wavefunctions of the 2D rigid rotor for m=1 and m=2 are orthogonal.

A: Answer is explained below.  The required condition for orthogonality is as follows:

Q: The Hamiltonian operator for H; in the Born-Oppenheimer approximation is ... 1 (A) H = +±V² 2 1 1 1…

A: For H2+, the system consists of 1 electron and 2 nuclei.

Q: 2.8(b) Calculate the probability that an O- bond treated as a harmonic oscillator will be found at a…

A: Solution -

Q: Using the commutator, verify or disprove that the momentum and position operators commute. What is…

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Q: Consider a spin-1/2 atom with spins up and down. For a system of N such localized atoms, Find the…

A: Answer is explained below.  We know, Atomic number of nitrogen is 7 and thus, electronic…

Q: Determine the probability of finding a particle ring in the 3rd excited state for the limits on a

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