Derive the constant A for a normalized one-dimensional Maxwellian. distribution f (u) = Aexp(-mu² /2KT) %3D such that f (u)du = 1

Q: using maxwell equations show that:  Cv=-T (∂2A/∂T2)v and Cp=-T (∂2G/∂T2)p  where A=Helmholtz free…

A: The Helmholtz free energy be defined as,

Q: (a) (vx), (b) (v). (c) (v²v.). (d) (v?v»),

A: For the ideal gas,nε=Nm2πkBT32 e-mv22kBT 4πv2

Q: Suppose that the probability of observing |0⟩ in the state |ϕ1⟩ is 1/4 and the probability of…

A:

Q: Let ¥₁ (x) and ↳₂2 (x) be normalized stationary states (energy eigenfunctions) of an one-…

A:

Q: Normalize the total wavefunction for a particle in a 2-d box: N sin ("): (") Na,ny (X, y) sin а for…

A:

Q: Calculate the uncertainties dr = V(r2) and dp = Vp?) for a particle confined in the region -a a, r…

A: As we can see the given wave function is normalised and in outside region it's zero. Therefore This…

Q: The wave function of a particle at time t=0 is given by|w(0)) = (u,) +|u2}), where |u,) and u,) are…

A:

Q: We have a free particle in one dimension at a time t = 0, the initial wave function is V (x,0) = Ae…

A:

Q: We have a free particle in one dimension at a time t = 0, the initial wave function is V (x, 0) =…

A: To answer the question, we first write the Normalization condition for a wave function, and then use…

Q: The wavefunction for a harmonic oscillator with v= 1 is given by: Vv-1 Ny 2y exp 2 Determine the…

A: I have use concept of mean value

Q: A particle with the energy E is incident from the left on a potential step of height Uo and a…

A: This problem is a combination of step and delta function. There are two regions here, one is x<0,…

Q: Calculate Z for a single oscillator in an Einstein solid at a temperature T = 2TE = 2Ɛ/kB.

A:

Q: The eigenfunctions satisfy the condition | Vi (x)m(x)dx = &nm , &nm = 1 if n %3D %3D = m , otherwise…

A:

Q: A wave function of a particle with mass m is given by, Acosa ≤ ≤+ otherwise b(z) = {1 Find the…

A: See step 2 .

Q: Evaluate the following expectation values: (a) ⟨ℓ,m1​∣Lx​∣ℓ,m2​⟩ (b) ⟨ℓ,m1​∣Ly​∣ℓ,m2​⟩

A:

Q: U = Uo U = (0 x = 0 A potential step U(x) is defined by U(x) = 0 for x 0 If an electron beam of…

A: Potential Step: A potential step U(x) is defined by, U(x)=0      for   x<0 U(x)=U0    for   x…

Q: Show that the expectation value for the speed of a particle, ( v ), is: = 8kBT πm using the…

A: We will first write expression for expectation value for speed of particle. Then we will we…

Q: Using the continuity condition of an acceptable wavefunction at x = a, find c and d in terms of a…

A: Wavefunction The wavefunction of a particle is a mathematical expression that encodes all the…

Q: Consider a particle of mass m moving in one dimension with wavefunction $(x) Vi for sin L - and zero…

A: The momentum operator is given by Therefore the operator is given by Where The given wave…

Q: A boat on the surface of the water suffers an explosion. Who hears the explosion first, a second…

A: Assume that a boat on the surface of the water suffers an explosion. The value of βwater = 2.2x109…

Q: Consider the wavefunction (4.5) with mi an integer and o < ¢< 2m. Find the normalization factor for…

A:

Q: Let y, (x) denote the orthonormal stationary states of a system corresponding to the energy En.…

A: Expectation value of energy

Q: We have a free particle in one dimension at a time t 0, the initial wave function is V(x,0) =…

A:

Q: Show that the Maxwell speed distribution function F(v) approaches zero by taking the limit as v → 0…

A: The air molecules surrounding us aren't all traveling at an equivalent speed, albeit the air is…