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For a particle of mass m, consider a Morse potential of V. V(x) cosh (Bx)' where...
2. Consider the bound states (E < 0) of a particle of mass u on the...
2. Consider the bound states (E < 0) of a particle of mass u on the one- dimensional half line, 0< x < oo, with the linear potential, b a + V () where a and b are positive constants (a) What is the asymptotic behavior of the wavefunction as x is useful to define a dimensionless variable. (Ans: ~e /24E/2).) oo. It where u= (b) What is the asymptotic behavior of the wavefunction as a - 0. (Ans: b~...
Instead of assuming that a one-dimensional particle has no energy (v(x)=0), consider the case of a...
Instead of assuming that a one-dimensional
particle has no energy (v(x)=0), consider the case of a
one-dimensional particle which has finite, but constant, energy
V(x)= V sub zero.. Show that the ID particle in a box wave
functions. n(x)= A sin ((pi n x)/a). Also solve the Schrödinger
equation for this potential, and determine the energies En
Problem 2: Particle in a Box with Non-Zero Energy (2 points) Instead of assuming that a one-dimensional particle has no energy (V(x) =...
A For a particle with mass m moving under a one dimensional potential V(x), one solution...
A For a particle with mass m moving under a one dimensional potential V(x), one solution to the Schrödinger equation for the region 0<x< oo is x) =2 (a>0), where A is the normalization constant. The energy of the particle in the given state is 0, Show that this function is a solution, and find the corresponding potential V(x)?
The potential in a region between x-0 and x = 6.00 m is V-a + bx,...
The potential in a region between x-0 and x = 6.00 m is V-a + bx, where a 12.8 V and b =-5.70 V/m. (a) Determine the potential at x = 0. Determine the potential atx- 3.00 m (b) Determine the magnitude and direction of the electric field at x 0. magnitude direction -Select- V/m Determine the magnitude and direction of the electric field at x 3.00 m magnitude V/m direction
The potential in a region between x 0 andx 6.00 m is V a t bx,...
The potential in a region between x 0 andx 6.00 m is V a t bx, where a 14.2 V and b-7.70 V/m. (a) Determine the potential at x = 0. Determine the potential at x 3.00 m Determine the potential at x 6.00 m. (b) Determine the magnitude and direction of the electric field at x = 0. magnitude direction Select V/m Determine the magnitude and direction of the electric field at x 3.00 m magnitude V/m direction Select...
2.5 ty which will be discussed in chapter 4 2.3 Consider a particle of mass m...
2.5
ty which will be discussed in chapter 4 2.3 Consider a particle of mass m subject to a one-dimensional potential V(x) that is given by V = 0, x <0; V = 0, 0<x<a; V = Vo, x> Show that bound (E < Vo) states of this system exist only if k cotka = -K where k2 = 2mE/12 and k' = 2m(Vo - E)/h4. 2.4 Show that if Vo = 974/2ma, only one bound state of the system...
1. A particle of mass m moves in the one-dimensional potential: x<-a/2 x>a/2 Sketch the potential....
1. A particle of mass m moves in the one-dimensional potential: x<-a/2 x>a/2 Sketch the potential. Sketch what the wave functions would look like for α = 0 for the ground state and the 1st excited state. Write down a formula for all of the bound state energies for α = 0 (no derivation necessary). a) b) Break up the x axis into regions where the Schrödinger equation is easy to solve. Guess solutions in these regions and plug them...
Consider a particle in a 1-d well with potential V(x) =-U for-d < x < d,...
Consider a particle in a 1-d well with potential V(x) =-U for-d < x < d, and V(z) 0 elsewhere. We will use the variational wave function v(z) = A(b + r), t(x)-A(b-x), -b < r < 0, 0 < x < b, to show that a bound state exists for any U0. a) Normalize the wave function. Find the expectation values of the kinetic and potential energies b) Show that for sufficiently large b, with b> d, the expectation...
A particle of mass m is bound by the spherically-symmetric three-dimensional harmonic- oscillator potential energy ,...
A particle of mass m is bound by the spherically-symmetric three-dimensional harmonic- oscillator potential energy , and ф are the usual spherical coordinates. (a) In the form given above, why is it clear that the potential energy function V) is (b) For this problem, it will be more convenient to express this spherically-symmetric where r , spherically symmetric? A brief answer is sufficient. potential energy in Cartesian coordinates x, y, and z as physically the same potential energy as the...
Q4. Consider the 1D infinite square-well potential shown in the figure below. V(x) O0 Position (a)...
Q4. Consider the 1D infinite square-well potential shown in the figure below. V(x) O0 Position (a) State the time-independent Schrödinger equation within the region 0<x<L for a particle with positive energy E 2 marks] (b) The wavefunction for 0<x< L can be written in the general form y(x) = Asin kx + B cos kx. Show that the normalised wavefunction for the 1D infinite potential well becomes 2sn'n? ?snT/where ( "1,2,3 ! where ( n = 1,2,5, ). [4 marks]...
2. Consider the bound states (E < 0) of a particle of mass u on the one- dimensional half line, 0< x < oo, with the linear potential, b a + V () where a and b are positive constants (a) What is the asymptotic behavior of the wavefunction as x is useful to define a dimensionless variable. (Ans: ~e /24E/2).) oo. It where u= (b) What is the asymptotic behavior of the wavefunction as a - 0. (Ans: b~...
Instead of assuming that a one-dimensional
particle has no energy (v(x)=0), consider the case of a
one-dimensional particle which has finite, but constant, energy
V(x)= V sub zero.. Show that the ID particle in a box wave
functions. n(x)= A sin ((pi n x)/a). Also solve the Schrödinger
equation for this potential, and determine the energies En
Problem 2: Particle in a Box with Non-Zero Energy (2 points) Instead of assuming that a one-dimensional particle has no energy (V(x) =...
A For a particle with mass m moving under a one dimensional potential V(x), one solution to the Schrödinger equation for the region 0<x< oo is x) =2 (a>0), where A is the normalization constant. The energy of the particle in the given state is 0, Show that this function is a solution, and find the corresponding potential V(x)?
The potential in a region between x-0 and x = 6.00 m is V-a + bx, where a 12.8 V and b =-5.70 V/m. (a) Determine the potential at x = 0. Determine the potential atx- 3.00 m (b) Determine the magnitude and direction of the electric field at x 0. magnitude direction -Select- V/m Determine the magnitude and direction of the electric field at x 3.00 m magnitude V/m direction
The potential in a region between x 0 andx 6.00 m is V a t bx, where a 14.2 V and b-7.70 V/m. (a) Determine the potential at x = 0. Determine the potential at x 3.00 m Determine the potential at x 6.00 m. (b) Determine the magnitude and direction of the electric field at x = 0. magnitude direction Select V/m Determine the magnitude and direction of the electric field at x 3.00 m magnitude V/m direction Select...
2.5
ty which will be discussed in chapter 4 2.3 Consider a particle of mass m subject to a one-dimensional potential V(x) that is given by V = 0, x <0; V = 0, 0<x<a; V = Vo, x> Show that bound (E < Vo) states of this system exist only if k cotka = -K where k2 = 2mE/12 and k' = 2m(Vo - E)/h4. 2.4 Show that if Vo = 974/2ma, only one bound state of the system...
1. A particle of mass m moves in the one-dimensional potential: x<-a/2 x>a/2 Sketch the potential. Sketch what the wave functions would look like for α = 0 for the ground state and the 1st excited state. Write down a formula for all of the bound state energies for α = 0 (no derivation necessary). a) b) Break up the x axis into regions where the Schrödinger equation is easy to solve. Guess solutions in these regions and plug them...
Consider a particle in a 1-d well with potential V(x) =-U for-d < x < d, and V(z) 0 elsewhere. We will use the variational wave function v(z) = A(b + r), t(x)-A(b-x), -b < r < 0, 0 < x < b, to show that a bound state exists for any U0. a) Normalize the wave function. Find the expectation values of the kinetic and potential energies b) Show that for sufficiently large b, with b> d, the expectation...
A particle of mass m is bound by the spherically-symmetric three-dimensional harmonic- oscillator potential energy , and ф are the usual spherical coordinates. (a) In the form given above, why is it clear that the potential energy function V) is (b) For this problem, it will be more convenient to express this spherically-symmetric where r , spherically symmetric? A brief answer is sufficient. potential energy in Cartesian coordinates x, y, and z as physically the same potential energy as the...
Q4. Consider the 1D infinite square-well potential shown in the figure below. V(x) O0 Position (a) State the time-independent Schrödinger equation within the region 0<x<L for a particle with positive energy E 2 marks] (b) The wavefunction for 0<x< L can be written in the general form y(x) = Asin kx + B cos kx. Show that the normalised wavefunction for the 1D infinite potential well becomes 2sn'n? ?snT/where ( "1,2,3 ! where ( n = 1,2,5, ). [4 marks]...
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