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Instructions. For each question, show all work leading to an answer and simplity as much as...
A) Calculate the mean values <x^2> and <p^2x> for stationery state n. B) Calculate the rms...
A) Calculate the mean values <x^2> and <p^2x> for
stationery state n.
B) Calculate the rms deviations sigma(x) and sigma(px) for
stationery state n. Check that the Heisenberg uncertainty principle
is satisfied.
1. Consider a particle of mass m in an infinite square well with potential energy 0 for 0 saSa otherwise. V (z) = For simplicity, we may take the 'universe' here to be the region of 0 sas a, which is where the wave function is nontrivial. Consequently,...
1. Consider a particle of mass m in an infinite square well with potential energy 0...
1. Consider a particle of mass m in an infinite square well with potential energy 0 for 0 Sz S a oo otherwise V (x) For simplicity, we may take the 'universe' here to be the region of 0 S z S a, which is where the wave function is nontrivial. Consequently, we may express stationary state n as where En is the associated mechanical energy. It can be shown that () a/2 and (p:)0 for stationary state n. (a)...
part (e),(f) and (g) 3. Wave functions (40 marks) Consider particle described by wave function (x)...
part (e),(f) and (g)
3. Wave functions (40 marks) Consider particle described by wave function (x) = Ce-x/a for x > 0, and otherwise (C is a real and non-negative). (a) Normalise (x) and plot it (you can use a computer to plotit). (b) Calculate the probability that the particle is located within distance a from the origin. (e) Find mean value of position measurement. (d) Find mean value of momentum measurement. Hint: use the fact that (x) is purely...
The initial wave function of a free particle is: Ψ(x,0) = A, for |x| = 0,...
The initial wave function of a free particle is: Ψ(x,0) = A, for |x| = 0, otherwise where a and A are positive real numbers. The particle is in a zero (or constant) potential environment since it is a free particle a) Determine A from normalization. b) Determine φ(p) = Φ(p,0), the time-zero momentum representation of the particle state. What is Φ(p,t)? Sketch φ(p). Locate the global maximum and the zeros of φ(p). Give the expression for the zeros (i.e.,...
Instructions. For each question, show al work leading to an answer and simplify as much as...
Instructions. For each question, show al work leading to an answer and simplify as much as reasonably possible. 1. Show that where u :-cos ? and the function H (u) is the Legendre polynomial of order 1. 2. The surface of a sphere of radius R carries an scalar potential kcos 30, where k is a constant. Other than a surface charge, no charge is present elsewhere (a) Find the scalar potential everywhere (b) Find the charge density ? (0)...
Instructions. For each question, show all work leading to an answer and simplify as much as...
Instructions. For each question, show all work leading to an answer and simplify as much as reasonably possible. 1. A 3.00-kg block starts from rest at the top of a ramp having an inclination of 30.0°. The block slides a distance of 2.00 m down the ramp in 1.50 s. Neglect air resistance. (a) Find the magnitude of the block's constant acceleration. (b) Find the coefficient of kinetic frictioti between block and ramp. 2. A small, flat cushion of mass...
Instructions. For each question, show all work leading to an answer and simplify as much as...
Instructions. For each question, show all work leading to an answer and simplify as much as reasonably possible. 1. An amusement-park ride consists of a large vertical cylinder of radius R. The cylinder spins about its axis fast enough such that any person inside is pinned against the wall when the floor drops away. Let p, be the coefficient of static friction between person and wall. Find the minimum speed that the cylinder wall must have to keep a person...
Need help solving Instructions. For each question, show all work leading to an answer and simplify...
Need help solving
Instructions. For each question, show all work leading to an answer and simplify as much as reasonably possible. 1. A 3.00-kg block starts from rest at the top of a ramp having an inclination of 30.0°. The block slides a distance of 2.00 m down the ramp in 1.50 s. Neglect air resistance (a) Find the magnitude of the block's constant acceleration (b) Find the coefficient of kinetic friction between block and ramp 2. A sal, flat...
Question 1: As you work through the parts of this question you are going to show...
Question 1: As you work through the parts of this question you are going to show that the Maxwell equations naturally contain electromagnetic waves. In a region of space that is void of all charges and currents, p=0 and J = 0 the Maxwell equations come out to be: Y E = 0 7.B=0 7 x Ē = -1 1 x B = Poco a) Using the same idea as I did in the lecture, derive the Wave Equation for...
Question 10 Statistical thermodynamics may be used to find the radiation pressure P for cavity (or...
Question 10 Statistical thermodynamics may be used to find the radiation pressure P for cavity (or black body) radiation in terms of the energy per unit volume u. (a) An ideal quantum gas comprises non-interacting identical particles with discrete quantum states labelled 1, 2, ...,r ,....The partition function is given by Z (T,V,N)- > exp(-B(n,&, + п,&, +...)} пп. (i) Define the symbols n1, n2,...,n,...and 81, 82, ..., Er,... (iiExplain why, for photons, the partition function may be expressed as:...
A) Calculate the mean values <x^2> and <p^2x> for
stationery state n.
B) Calculate the rms deviations sigma(x) and sigma(px) for
stationery state n. Check that the Heisenberg uncertainty principle
is satisfied.
1. Consider a particle of mass m in an infinite square well with potential energy 0 for 0 saSa otherwise. V (z) = For simplicity, we may take the 'universe' here to be the region of 0 sas a, which is where the wave function is nontrivial. Consequently,...
1. Consider a particle of mass m in an infinite square well with potential energy 0 for 0 Sz S a oo otherwise V (x) For simplicity, we may take the 'universe' here to be the region of 0 S z S a, which is where the wave function is nontrivial. Consequently, we may express stationary state n as where En is the associated mechanical energy. It can be shown that () a/2 and (p:)0 for stationary state n. (a)...
part (e),(f) and (g)
3. Wave functions (40 marks) Consider particle described by wave function (x) = Ce-x/a for x > 0, and otherwise (C is a real and non-negative). (a) Normalise (x) and plot it (you can use a computer to plotit). (b) Calculate the probability that the particle is located within distance a from the origin. (e) Find mean value of position measurement. (d) Find mean value of momentum measurement. Hint: use the fact that (x) is purely...
Instructions. For each question, show al work leading to an answer and simplify as much as reasonably possible. 1. Show that where u :-cos ? and the function H (u) is the Legendre polynomial of order 1. 2. The surface of a sphere of radius R carries an scalar potential kcos 30, where k is a constant. Other than a surface charge, no charge is present elsewhere (a) Find the scalar potential everywhere (b) Find the charge density ? (0)...
Instructions. For each question, show all work leading to an answer and simplify as much as reasonably possible. 1. A 3.00-kg block starts from rest at the top of a ramp having an inclination of 30.0°. The block slides a distance of 2.00 m down the ramp in 1.50 s. Neglect air resistance. (a) Find the magnitude of the block's constant acceleration. (b) Find the coefficient of kinetic frictioti between block and ramp. 2. A small, flat cushion of mass...
Instructions. For each question, show all work leading to an answer and simplify as much as reasonably possible. 1. An amusement-park ride consists of a large vertical cylinder of radius R. The cylinder spins about its axis fast enough such that any person inside is pinned against the wall when the floor drops away. Let p, be the coefficient of static friction between person and wall. Find the minimum speed that the cylinder wall must have to keep a person...
Need help solving
Instructions. For each question, show all work leading to an answer and simplify as much as reasonably possible. 1. A 3.00-kg block starts from rest at the top of a ramp having an inclination of 30.0°. The block slides a distance of 2.00 m down the ramp in 1.50 s. Neglect air resistance (a) Find the magnitude of the block's constant acceleration (b) Find the coefficient of kinetic friction between block and ramp 2. A sal, flat...
Question 1: As you work through the parts of this question you are going to show that the Maxwell equations naturally contain electromagnetic waves. In a region of space that is void of all charges and currents, p=0 and J = 0 the Maxwell equations come out to be: Y E = 0 7.B=0 7 x Ē = -1 1 x B = Poco a) Using the same idea as I did in the lecture, derive the Wave Equation for...
Question 10 Statistical thermodynamics may be used to find the radiation pressure P for cavity (or black body) radiation in terms of the energy per unit volume u. (a) An ideal quantum gas comprises non-interacting identical particles with discrete quantum states labelled 1, 2, ...,r ,....The partition function is given by Z (T,V,N)- > exp(-B(n,&, + п,&, +...)} пп. (i) Define the symbols n1, n2,...,n,...and 81, 82, ..., Er,... (iiExplain why, for photons, the partition function may be expressed as:...
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