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Derive the following commutators: [x, P_x] [x, P_y] [P_x, P_x] [x, T_x] [P_x, T_x] Can both...
both pls 1) Which of the following operator(s) is/are Hermitian? a) id/dy? b) d/dy2 c) id/dy...
both pls
1) Which of the following operator(s) is/are Hermitian? a) id/dy? b) d/dy2 c) id/dy You may assume that the functions on which these operators operate are appropriately well behaved at infinity. (Hint #1: .. P dy = f. y pudy where the integral hudu = Uv - Sudv. Hint #2: Use y = e) 2) In each case below show (in the space provided directly) that F(y) is an eigen- function of the operator A and find the...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can'...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
Problem 3. Consider two atoms with masses mi and m2, each moving along the x-direction, and that are connected by a har...
Problem 3. Consider two atoms with masses mi and m2, each moving along the x-direction, and that are connected by a harmonic spring with spring constant k and equilibrium length lo: mi m2 Ömimo → X1 X2 The Hamiltonian operator for this system is ÎN = Pí 1 2 1 2 +5k (ĉ2 – ĉ1 – 10)? 2m2' 2" 2m, and the time-independent Schrödinger equation for the two-atom wavefunction (x1, x2) is ÊV(21, x2) = EV (21, x2) This equation...
Consider a potential well defined as U(x) = for x < 0, U(x) = 0 for 0 < x < L, and U(x) = U0 > 0 for x > L (see the following figure).
Consider a potential well defined as \(U(x)=\infty\) for \(x<0, U(x)=0\)for \(0<x<L,\)and \(U(x)=U_{0}>0\) for \(x>L\) (see the following figure). Consider a particle with mass \(m\) and kinetic energy \(E<U_{0}\)that is trapped in the well. (a) The boundary condition at the infinite wall ( \(x=\)0) is \(\psi(x)=0\). What must the form of the function \(\psi(x)\) for \(0<x<L\)be in order to satisfy both the Schrödinger equation and this boundary condition? (b) The wave function must remain finite as \(x \rightarrow \infty\). What must...
12. Which of the following sets of quantum numbers ( n, l, m l,ms) is not...
12. Which of the following sets of quantum numbers ( n, l, m l,ms) is not allowed? a. 2 1 0 + b. 2 2 1 + c. 3 1 0 – d. 5 0 0 + e. 4 2 –1 – 14. Which of the following atoms is the most electronegative? a. Al b. B c. Cs d. N e. Na 15. The Pauli exclusion principle states that a. an electron can have either particle character or wave character. b. no two electrons in the same atom can have the...
1.Which one of the 0.1 M solutions of C2H5OH, HC2H3O2 and NaC2H3O2, in water will cause...
1.Which one of the 0.1 M solutions of C2H5OH, HC2H3O2 and NaC2H3O2, in water will cause of the light bulb to glow most brightly? 2.For a functional group having a carbon atom singly bonded to an electronegative atom, (a) this carbon atom is likely to bear a partial positive charge. (b) bonding electrons are to be delocalized within this functional group (c) it appears as an essential part of ester molecules. (d) it appears as an essential part of ketone...
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3.1 Rotations and Angular-Momentum Commutation Relations 159 We are particularly interested in an infinitesimal form of Ry: (3.1.4) where terms of order & and higher are ignored. Likewise, we have R0= ° :- R(E) = 1 (3.1.5) and (3.1.5b) - E01 which may be read from (3.1.4) by cyclic permutations of x, y, zthat is, x y , y → 2,2 → x....
Learning Goal: To understand the relationship between force, impulse, and momentum. The effect of a net...
Learning Goal: To understand
the relationship between force, impulse, and momentum. The effect
of a net force ΣF⃗ acting on an object is related both to the force
and to the total time the force acts on the object. The physical
quantity impulse J⃗ is a measure of both these effects. For a
constant net force, the impulse is given by J⃗ =F⃗ Δt. The impulse
is a vector pointing in the same direction as the force vector. The
units...
Problem 7 A satellite consists two cylinders which can rotate relative to each other about the common axis of summetry. The rotation can be precisely controlled through a built-in motor. Both cyllind...
Problem 7 A satellite consists two cylinders which can rotate relative to each other about the common axis of summetry. The rotation can be precisely controlled through a built-in motor. Both cyllinders can be asuumed to be uniform; they have the same mass, m 10.0 kg, and the same radius 0.30 m. The top cylinder has attached to it two balls, each of which has mass 1.0kg and radius b 0.1 m. Each ball is fastened to the end of...
1-5 250 11/20/2019 Test his worth problem por n o larger the problem estis 1-5 year o f There are will he graded on...
1-5
250 11/20/2019 Test his worth problem por n o larger the problem estis 1-5 year o f There are will he graded on the first throw odred ) Questions 1-5: Circle the BEST wwer to each The metric for linear momenti The metric unit for power bm's Iracar suddenly doubles its speed from 10' to 60m, what happens to its linear momentum? at screases by a factor of 2 b it increases by a factor of 4 c. increases...
both pls
1) Which of the following operator(s) is/are Hermitian? a) id/dy? b) d/dy2 c) id/dy You may assume that the functions on which these operators operate are appropriately well behaved at infinity. (Hint #1: .. P dy = f. y pudy where the integral hudu = Uv - Sudv. Hint #2: Use y = e) 2) In each case below show (in the space provided directly) that F(y) is an eigen- function of the operator A and find the...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
Problem 3. Consider two atoms with masses mi and m2, each moving along the x-direction, and that are connected by a harmonic spring with spring constant k and equilibrium length lo: mi m2 Ömimo → X1 X2 The Hamiltonian operator for this system is ÎN = Pí 1 2 1 2 +5k (ĉ2 – ĉ1 – 10)? 2m2' 2" 2m, and the time-independent Schrödinger equation for the two-atom wavefunction (x1, x2) is ÊV(21, x2) = EV (21, x2) This equation...
Use the following information
To help you solve the following questions. Show all
work for thumbs up.
3.1 Rotations and Angular-Momentum Commutation Relations 159 We are particularly interested in an infinitesimal form of Ry: (3.1.4) where terms of order & and higher are ignored. Likewise, we have R0= ° :- R(E) = 1 (3.1.5) and (3.1.5b) - E01 which may be read from (3.1.4) by cyclic permutations of x, y, zthat is, x y , y → 2,2 → x....
Learning Goal: To understand
the relationship between force, impulse, and momentum. The effect
of a net force ΣF⃗ acting on an object is related both to the force
and to the total time the force acts on the object. The physical
quantity impulse J⃗ is a measure of both these effects. For a
constant net force, the impulse is given by J⃗ =F⃗ Δt. The impulse
is a vector pointing in the same direction as the force vector. The
units...
Problem 7 A satellite consists two cylinders which can rotate relative to each other about the common axis of summetry. The rotation can be precisely controlled through a built-in motor. Both cyllinders can be asuumed to be uniform; they have the same mass, m 10.0 kg, and the same radius 0.30 m. The top cylinder has attached to it two balls, each of which has mass 1.0kg and radius b 0.1 m. Each ball is fastened to the end of...
1-5
250 11/20/2019 Test his worth problem por n o larger the problem estis 1-5 year o f There are will he graded on the first throw odred ) Questions 1-5: Circle the BEST wwer to each The metric for linear momenti The metric unit for power bm's Iracar suddenly doubles its speed from 10' to 60m, what happens to its linear momentum? at screases by a factor of 2 b it increases by a factor of 4 c. increases...
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