Write expressions for the following operators operators for a particle in a box 1) Position operator...
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Write expressions for the following operators operators for a
particle in a box
1) Position operator...
(2.) Consider the orbital angular momentum operator defined in terms of the position and momentum operators...
(2.) Consider the orbital angular momentum operator defined in terms of the position and momentum operators as p. Define the angular momentum raising and lowering operators as L± = LztiLy. Use the commutation relations for the position and m omentum operators and find the commutators for: (a.) Lx, Lz and Ly, Lz; (b.) L2, Lz; (c.) L+,L
3. Using position and momentum operators prove that <xp> = -<px> = ihbar/2 for the infinite...
3. Using position and momentum operators prove that <xp>
= -<px> = ihbar/2 for the infinite potential energy well
wavefunctions.
4. Consider two operators defined as A+ and A-
any help with 3 and 4 would be greatly appreciated!!!
3. Using position and momentum operators prove that (xp) = -(p.c) = for the infinite potential energy well wavefunctions. 4. Consider two operators defined as A+ = a (- + oʻx) and A- = a (-de-a²x), where a = w and...
A particle of mass m is subject to a doubly infinite square well, with widths L,...
A particle of mass m is subject to a doubly infinite square well, with widths L, located at (a/2, a/2). The eigenstate wave functions for this are v(x, y) = L, = a and centre %3D %3D sin () sin ("). nyTy a) Find an expression for the position operator in bra-ket notation. b) Find an expression for the momentum operator in bra-ket notation. c) The particle is initially in the state |) : for position and momentum to find...
Particle in a box Figure 1 is an illustration of the concept of a particle in...
Particle in a box Figure 1 is an illustration of the concept of a particle in a box. V=00 V=00 V=0 Figure 1. A representation of a particle in a box, where the potential energy, V, is zero between x = 0 and x = L and rises abruptly to infinity at the walls. The Schrödinger equation for a particle in a box reads t² d²u Y +V(x)y = Ey 2m dx2 + (1) where ħ=h/21 , y represents the...
#4 4) Show that: a) The classical kinetic energy = (1/2). muy is equal to py/2m. Here py is the linear momentum in t...
#4
4) Show that: a) The classical kinetic energy = (1/2). muy is equal to py/2m. Here py is the linear momentum in the y-direction. b) Show that the Classical kinetic energy operator (1/2).muy is equal to the quantum mechanical kinetic energy operator = -1°/8x'm d/dy?. (Hints: Use the definition for momentum operator of the particle py=- (ih/2x) d/dy in quantum mechanics). c) Determine if A and B commute: if A = d/dy?, B = y, and f(y) = 30y...
Q 1: For particle in a box problem, answer the following questions, a) Why n=0 is...
Q 1: For particle in a box problem, answer the following questions, a) Why n=0 is not an allowed quantum number? b) En = 0 is not allowed for particle in a box, why? c) Ground state wavefunction is orthogonal to the first excited state wavefunction, what does it mean? Q 2: An electronic system that is treated as particle in 3-D box with dimensions of 3Å x 3Å x 4Å. Calculate the wavelength corresponding to the lowest energy transition...
1: For a free particle, U(x)-0, in the state Ψ(x)-e®, determine if the particle is in...
1: For a free particle, U(x)-0, in the state Ψ(x)-e®, determine if the particle is in an eigenstate of the following operators and give the eigenvalue if it is. a position z m b. momentum c. Energy d. Translation (D)
5. The relativistic corrections to the energy of a particle can be estimated by applying a...
5. The relativistic corrections to the energy of a particle can be estimated by applying a fictitious "external potential” V = -p4/8m'c>, where p is the momentum of the particle, m is its mass, and c is the ħ d speed of light. Replacing p with its operator (p= ), the corresponding operator for the "external potential" is = - a . Is the ground state wavefunction of the particle in a box ( sin (**)) an eigenfunction of the...
1. Using logical operators modify the following Python "if" statement to print ("AND operator condition worked")?...
1. Using logical operators modify the following Python "if" statement to print ("AND operator condition worked")? x=2 y=3 if (x<=2 or y>=3) and (x>2 or y<2): print("AND operator condition worked") else: print("it doesn't work") 2. Write a program that asks user for five numbers and returns the largest of them. Do not use max function built in python.
Derive the following commutators: [x, P_x] [x, P_y] [P_x, P_x] [x, T_x] [P_x, T_x] Can both...
Derive the following commutators: [x, P_x] [x, P_y] [P_x, P_x] [x, T_x] [P_x, T_x] Can both the position and momentum of the particle in the same direction be known precisely? Can both the position and kinetic energy of the particle in the same direction be known precisely? Determine whether the following operators are Hermitian Operators. You may assume that the functions on which these operators operate behave properly in the limit of plusminus x rightarrow infinity. [see McQuarrie section 4-5]...
(2.) Consider the orbital angular momentum operator defined in terms of the position and momentum operators as p. Define the angular momentum raising and lowering operators as L± = LztiLy. Use the commutation relations for the position and m omentum operators and find the commutators for: (a.) Lx, Lz and Ly, Lz; (b.) L2, Lz; (c.) L+,L
3. Using position and momentum operators prove that <xp>
= -<px> = ihbar/2 for the infinite potential energy well
wavefunctions.
4. Consider two operators defined as A+ and A-
any help with 3 and 4 would be greatly appreciated!!!
3. Using position and momentum operators prove that (xp) = -(p.c) = for the infinite potential energy well wavefunctions. 4. Consider two operators defined as A+ = a (- + oʻx) and A- = a (-de-a²x), where a = w and...
A particle of mass m is subject to a doubly infinite square well, with widths L, located at (a/2, a/2). The eigenstate wave functions for this are v(x, y) = L, = a and centre %3D %3D sin () sin ("). nyTy a) Find an expression for the position operator in bra-ket notation. b) Find an expression for the momentum operator in bra-ket notation. c) The particle is initially in the state |) : for position and momentum to find...
Particle in a box Figure 1 is an illustration of the concept of a particle in a box. V=00 V=00 V=0 Figure 1. A representation of a particle in a box, where the potential energy, V, is zero between x = 0 and x = L and rises abruptly to infinity at the walls. The Schrödinger equation for a particle in a box reads t² d²u Y +V(x)y = Ey 2m dx2 + (1) where ħ=h/21 , y represents the...
#4
4) Show that: a) The classical kinetic energy = (1/2). muy is equal to py/2m. Here py is the linear momentum in the y-direction. b) Show that the Classical kinetic energy operator (1/2).muy is equal to the quantum mechanical kinetic energy operator = -1°/8x'm d/dy?. (Hints: Use the definition for momentum operator of the particle py=- (ih/2x) d/dy in quantum mechanics). c) Determine if A and B commute: if A = d/dy?, B = y, and f(y) = 30y...
1: For a free particle, U(x)-0, in the state Ψ(x)-e®, determine if the particle is in an eigenstate of the following operators and give the eigenvalue if it is. a position z m b. momentum c. Energy d. Translation (D)
5. The relativistic corrections to the energy of a particle can be estimated by applying a fictitious "external potential” V = -p4/8m'c>, where p is the momentum of the particle, m is its mass, and c is the ħ d speed of light. Replacing p with its operator (p= ), the corresponding operator for the "external potential" is = - a . Is the ground state wavefunction of the particle in a box ( sin (**)) an eigenfunction of the...
Derive the following commutators: [x, P_x] [x, P_y] [P_x, P_x] [x, T_x] [P_x, T_x] Can both the position and momentum of the particle in the same direction be known precisely? Can both the position and kinetic energy of the particle in the same direction be known precisely? Determine whether the following operators are Hermitian Operators. You may assume that the functions on which these operators operate behave properly in the limit of plusminus x rightarrow infinity. [see McQuarrie section 4-5]...
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