The potential of a particle is given as V (x) = -Vδ (x), with V being...

The potential of a particle is given as V (x) = -Vδ (x), with V being a positive number. Find the wave function and energy of the bounded states of this particle.

Expert Solution

In question given potential is V(x)=V (x).

In calcination I use potential V(x)=(x). (To distinguish Left hand side V and Right hand side V.)

genius_generous answered 8 months ago

The Langevin equation for a particle in 1 dimension in an external potential V (x) is:...

The Langevin equation for a particle in 1 dimension in an external potential V (x) is: mx'' =-(dV(x)/dx)-ξx'+F(t), where ξ is the friction constant, and F(t) is the random force.Take V (x) to be harmonic: V (x) = (m/2)ω^2x^2 .Find the general solution x(t) for arbitrary initial conditions and calculate the equilibrium time correlation function C(t) = <x(t)x(0)>.

Consider a particle moving in two spatial dimensions, subject to the following potential: V (x, y)...

Consider a particle moving in two spatial dimensions, subject to the following potential: V (x, y) = ( 0, 0 ≤ x ≤ L & 0 ≤ y ≤ H ∞, otherwise. (a) Write down the time-independent Schr¨odinger equation for this case, and motivate its form. (2) (b) Let k 2 = 2mE/~ 2 and rewrite this equation in a simpler form. (2) (c) Use the method of separation of variables and assume that ψ(x, y) = X(x)Y (y). Rewrite...

A particle is moving with the given data. Find the position of the particle. v(t) =...

A particle is moving with the given data. Find the position of the particle. v(t) = sin(t) − cos(t), s(0) = 4

Bound state in potential. Where V(x)=inf for x<0 V(x)=0 for 0 ≤ x ≤ L V...

Bound state in potential. Where V(x)=inf for x<0 V(x)=0 for 0 ≤ x ≤ L V (x) = U for x > L Write down the Schrödingerequation and solutions (wavesolutions) on general form for the three V(x).

A particle is moving according to the given data v(t)=t^2 - sqrt(t), x(0) = 0, 0...

A particle is moving according to the given data v(t)=t^2 - sqrt(t), x(0) = 0, 0 ≤ t ≤ 4. • Find x(t), the position of the particle at time t. • For what values of t is the particle moving to the left? To the right? • Find the displacement of the particle. • Find the total distance covered by the particle.

Consider the “step” potential: V(x) = 0 if x ≤ 0 = V0 if...

Consider the “step” potential: V(x) = 0 if x ≤ 0 = V0 if x ≥ 0 (a) Calculate the reflection coefficient for the case E < V0 , and (b) for the case E > V0.

We have potential of V (x) = ( 0, 0 ≤ x ≤ a. ∞, elsewhere....

We have potential of V (x) = ( 0, 0 ≤ x ≤ a. ∞, elsewhere. a) Find the ground state energy and the first and second excited states, if an electron is enclosed in this potential of size a = 0.100 nm. b) Find the ground state energy and the first and second excited states, if a 1 g metal sphere is enclosed in this potential of size a = 10.0 cm. c) Are the quantum effects important for...

The potential in a region between x = 0 and x = 6.00 m is V...

The potential in a region between x = 0 and x = 6.00 m is V = a + bx, where a = 12.6 V and b = -7.90 V/m. (a) Determine the potential at x = 0. ______ V Determine the potential at x = 3.00 m. ______ V Determine the potential at x = 6.00 m. ______ V (b) Determine the magnitude and direction of the electric field at x = 0. magnitude ________ V/m direction +x or...

Consider the step potential V (x) = 0 x ≤ 0 (I) = V0 x >...

Consider the step potential V (x) = 0 x ≤ 0 (I) = V0 x > 0 (II) . (a) What does the wave function for the scattering problem with 0 < E < V0 look like in regions I and II? (Write the equation for the wave functions, including only terms with non-zero coeﬃcients.) (b) What are the boundary conditions for the wave function and its derivative at x = 0? Deﬁne constants you are using (e.g., κ, k,...

An infinite potential well in one dimension for 0 ≤ x ≤ a contains a particle...

An infinite potential well in one dimension for 0 ≤ x ≤ a contains a particle with the wave function ψ = Cx(a − x), where C is the normalization constant. What is the probability wn for the particle to be in the nth eigenstate of the innite potential well? Find approximate numerical values for w1, w2 and w3.

Question