Consider the one dimensional model of one-particle-in-a-box. Under what condition the two quantum levels are orthogonal....

Consider the one dimensional model of one-particle-in-a-box. Under what condition the two quantum levels are orthogonal. Namely, find the relation between m and n so that < m | n > = 0

Expert Solution

queen_honey_blossom answered 2 years ago

Use the quantum particle wavefunctions for the kinetic energy levels in a one dimensional box to...

Use the quantum particle wavefunctions for the kinetic energy levels in a one dimensional box to qualitatively demonstrate that the classical probability distribution (any value of x is equally allowed) is obtained for particles at high temperatures.

Consider a particle of mass m confined to a one-dimensional box of length L and in...

Consider a particle of mass m confined to a one-dimensional box of length L and in a state with normalized wavefunction. For a partide in a box the energy is given by En = n2h2/8mL2 and, because the potential energy is zero, all of this energy is kinetic. Use this observation and, without evaluating any integrals, explain why < px2>= n2h2/4L2

5. Consider a particle in a two-dimensional, rigid, square box with side a. (a) Find the...

5. Consider a particle in a two-dimensional, rigid, square box with side a. (a) Find the time independent wave function φ(x,y)describing an arbitrary energy eigenstate. (b)What are the energy eigenvalues and the quantum numbers for the three lowest eigenstates? Draw the energy level diagram

Consider a particle of mass m that can move in a one-dimensional box of size L...

Consider a particle of mass m that can move in a one-dimensional box of size L with the edges of the box at x=0 and x = L. The potential is zero inside the box and infinite outside. You may need the following integrals: ∫ 0 1 d y sin ⁡ ( n π y ) 2 = 1 / 2 , for all integer n ∫ 0 1 d y sin ⁡ ( n π y ) 2 y = 1...

Solve the schordingers equation for a particle in a rigid two-dimensional box.

Use the one-dimensional particle-in-a-box model with impenetrable walls and the equation R = R_0*A^(1/3) to estimate...

Use the one-dimensional particle-in-a-box model with impenetrable walls and the equation R = R_0*A^(1/3) to estimate the minimum kinetic energy of a nucleon in a nucleus. Express your answer in MeV and in terms of a number 'n' the mass number 'A', and an exponent p, which is the ratio of two integers, resulting in K = n/A^p.

Using the particle in the 1-D box model, estimate the first 4 energy levels of the...

Using the particle in the 1-D box model, estimate the first 4 energy levels of the π-network in hexatriene, C6H8 (H2C=CH–CH=CH–CH=CH2). To calculate the box length, assume that the molecule is linear and use the values 135 and 154 pm for the C=C and C–C bonds, respectively. Only 2 out of the 6 ‘π-electrons’ of the 6 C-atoms can occupy each energy level (Pauli exclusion principle). Ignore the rest of the electrons (forming the core and the ??-bonding network). Sketch...

Consider a two-dimensional triangular lattice described by the two primitive vectors (in an orthogonal coordinate system...

Consider a two-dimensional triangular lattice described by the two primitive vectors (in an orthogonal coordinate system Find the two primitive lattice vectors describing the reciprocal lattice. Find the area of the 1st Brillouin zone and its relation with the area of the direct lattice unit cell.

For two dimensional particle in a box, how many electrons can we get at most in...

For two dimensional particle in a box, how many electrons can we get at most in the first energy level and why?

Consider a particle that is conﬁned by a one dimensional quadratic (harmonic) potential of the form...

Consider a particle that is conﬁned by a one dimensional quadratic (harmonic) potential of the form U(x) = Ax2 (where A is a positive real number). a) What is the Hamiltonian of the particle (expressed as a function of velocity v and x)? b) What is the average kinetic energy of the particle (expressed as a function of T)? c) Use the Virial Theorem (Eq. 1.46) to obtain the average potential energy of the particle. d) What would the average...

Question