3

WORKQUT PROBLEM #2A) Given 0f = x2 f ,is 0 a linear operator? ShowalLwork leading to conclusion: B) Do linear momentum operator p and position operator x commute? S...

Question

WORKQUT PROBLEM #2A) Given 0f = x2 f ,is 0 a linear operator? ShowalLwork leading to conclusion: B) Do linear momentum operator p and position operator x commute? Showall work leading to conclusion for why yes or why no. Recall: pf(x) = [email protected], xfkx) =xflx), commutator operator is [p,xJf (x) = pxf(x) Xpf(x).

WORKQUT PROBLEM #2 A) Given 0f = x2 f ,is 0 a linear operator? ShowalLwork leading to conclusion: B) Do linear momentum operator p and position operator x commute? Showall work leading to conclusion for why yes or why no. Recall: pf(x) = [email protected], xfkx) =xflx), commutator operator is [p,xJf (x) = pxf(x) Xpf(x).



Answers

Show that the operators for the $x$ coordinate and for the momentum in the $x$ direction $p_{x}$ do not commute. Calculate the operator representing the commutator of $x$ and $p_{x}$.

So we're continuing on with quantum chemistry. They were taking a look at communicators off to operators. That is as follows a happy hot people toe a be subtract B a on if a B equals zero Daniel then the operators or have commuted. So we have a few different equations that we need to consider next of all, hot X equals negative I h bra. Why? He said, Subtract said t do you buy? So then we have the exact same full wow the exact same form of equation. But why on said how we're just But we're just changing up the coordinates that were using the equations. What we find is that the commuter off l X l Y is equal to I H bar. Well said right?

Already. So today we are looking at or rather here. We're looking at three matrices which come from quantum physics. Eso we have Sigma one equals 0110 signal to equal zero I negative I zero saying my three equals 100 negative one and we have three equations that we need to verify using these three major cities. So we just go through and do our matrix multiplication. So for the product of two matrices, the IJ eighth element is going to be the dot product of Row I from the Left and Matrix with column J on the right hand matrix. So element 11 here is going to be zero time zero plus one times I, which is I element to one, is going to be one time zero plus zero times I. That's just zero element 120 times negative. I just still zero plus one time +00 element to two is going to you one times negative. I plus zero times zero. So we have negative I there and we need this. We need to see if that's equal to I Time Sigma three. Well, we can see we have a common factor of I here. We can just factor that out. So we have I times 100 negative one, which is I Time signal three. Next up, element 11 is going to be zero timeto one plus negative. I time zero. That's gonna be zero elements to one. It's I times one plus zero times zero. That's gonna be I. Element 12 is going to zero time zero plus negative I times negative one. We have a double negative. That's going to be a positive I there and element to two is going to be I time 00 times naked 10 And does that equal I Time signal one. Well, if we factor out the I and thats I times 0110 which is in fact, I time signal one. Lastly, we have down here. No 11 is going to one time. Zero plus zero times. One that's zero element to one is going to be zero time zero plus negative one times one. So it's a negative one down there. I want one too. Is going to you one time zero plus zero times. Sorry. One times one plus zero times zero. So that's going to be a one down there. An element to two is going to be zero times one plus negative one time zero. That's zero. We need to check. Does that equal? I time signal to. So if we look at ah Sigma two up there one second here. So sigma to is zero. I negative, I zero. We multiply this by I We need to keep in mind that when we multiply, I buy I When we have I squared, that is negative one. So we'd have I times I down here so we'd have negative one there, we'd have negative I squared up here zero But I squared is negative one. So we have negative negative one. But that means we have a double negative. That's just going to be positive one So we can see that. Yeah, that is, in fact, equal to I Time Sigma to


Similar Solved Questions

5 answers
0.5 m0.5 m1.5 m0.25 mOrigin0.75 m
0.5 m 0.5 m 1.5 m 0.25 m Origin 0.75 m...
5 answers
Required information NOTE: This is & multi-part question: Once an answer is submitted, You will be unable to return to this part: Consider the given figure_ Given P: = 540 N. 800 N40970*30o250Determine the x; Y, and components of the 540-N forceThe X component of the 540-N force is The y component of the 540-N force is The Z component of the 540-N force is
Required information NOTE: This is & multi-part question: Once an answer is submitted, You will be unable to return to this part: Consider the given figure_ Given P: = 540 N. 800 N 409 70* 30o 250 Determine the x; Y, and components of the 540-N force The X component of the 540-N force is The y c...
5 answers
Finding the Interval of Convergence n!(x c)" 1 .3 .5 (2n
Finding the Interval of Convergence n!(x c)" 1 .3 .5 (2n...
5 answers
2 Using the data you obtained from the graph in the previous problem determine the concentration of cobalt (II) in 1.975 g sample of a substance, which was dissolved in water in a 100 mL volumetric flask and then diluted to the mark. For the absorbance of the cobalt solution from the flask a value of 0.55 was obtained. What is the percentage of cobalt in the unknown compound? Atomic mass of Co is 58.933.
2 Using the data you obtained from the graph in the previous problem determine the concentration of cobalt (II) in 1.975 g sample of a substance, which was dissolved in water in a 100 mL volumetric flask and then diluted to the mark. For the absorbance of the cobalt solution from the flask a value o...
5 answers
(2y^2 x^2 Jdx xy dy = 0 Find the general solution: Write down the methed You use_
(2y^2 x^2 Jdx xy dy = 0 Find the general solution: Write down the methed You use_...
4 answers
Find the function $y=a x^{2}+b x+c$ whose graph contains the points $(1,2),(-2,-7),$ and (2,-3).
Find the function $y=a x^{2}+b x+c$ whose graph contains the points $(1,2),(-2,-7),$ and (2,-3)....
1 answers
$-A 5.00 \times 10^{5}-\mathrm{kg}$ rocket is accelerating straight up. Its engines produce $1.250 \times 10^{7} \mathrm{N}$ of thrust, and air resistance is $4.50 \times 10^{6} \mathrm{N}$. What is the rocket's acceleration? Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton's laws of motion.
$-A 5.00 \times 10^{5}-\mathrm{kg}$ rocket is accelerating straight up. Its engines produce $1.250 \times 10^{7} \mathrm{N}$ of thrust, and air resistance is $4.50 \times 10^{6} \mathrm{N}$. What is the rocket's acceleration? Explicitly show how you follow the steps in the Problem-Solving Strat...
4 answers
The moment of inertia about the origin for a lamina in the shape of' region R is given by the integral JS,(x2 y2) p(x,y) dA_ where p(x,Y) is the density function. Set up polar double integral t0 find thc moment of inertia for the part ofthe ring in the first and second quadrant between the lines and v3r and the circles 16 and r 100 where the density function is given by plx,y) = (x+y2)'_ Do not evaluate. (10 points)
The moment of inertia about the origin for a lamina in the shape of' region R is given by the integral JS,(x2 y2) p(x,y) dA_ where p(x,Y) is the density function. Set up polar double integral t0 find thc moment of inertia for the part ofthe ring in the first and second quadrant between the line...
5 answers
Iniemot provider Is trying (0 Qain advertising dexts and claimns thal Ihe meun ting & cuslomar sponds orlia Vule Caim po doy # quatel mnn 22 mendon Yotnan Eladlottodl How Eoula You wila tno null and altornative hypoutosos o ropresont ttu Intultol proxkder AMd want (6) How wouk you wrilo tho null and aitornative hypolhoses M VoU roprosent M compolim rOverigar d ntr Fopgort he I dhn? rejeci chimz(bitlt
Iniemot provider Is trying (0 Qain advertising dexts and claimns thal Ihe meun ting & cuslomar sponds orlia Vule Caim po doy # quatel mnn 22 mendon Yotnan Eladlottodl How Eoula You wila tno null and altornative hypoutosos o ropresont ttu Intultol proxkder AMd want (6) How wouk you wrilo tho null...
5 answers
51) 10g23.2 4 4e92 '00 Log25
51) 10g23.2 4 4e92 '00 Log25...
5 answers
Quastlon Assume that the number of insurance claims, N, filed in E (N) = 1OOOO. Use the normal year is Poisson distributed with P (IN - E(N) 300) approximation to the Poisson distribution to approximateST426J3_2020_Sc_Pafto SearchDALF1oFae PeiserF12 NsenWERU5FGAKXVBNMAltCtri
Quastlon Assume that the number of insurance claims, N, filed in E (N) = 1OOOO. Use the normal year is Poisson distributed with P (IN - E(N) 300) approximation to the Poisson distribution to approximate ST426J3_2020_Sc_Paf to Search DAL F1o Fae Peiser F12 Nsen W E R U 5 F G A K X V B N M Alt Ctri...
5 answers
+ 3) dz 2 4. 24
+ 3) dz 2 4. 24...
5 answers
"asuodsaJ S/4 J^ES IIIM uopsanb Jayjoue 01 BuMOW!llnoujag S! A{xkva =Zvf {x}va+ ^ ajqexedas S! {Kz+xhva = Kx "P aiqejedas s! K + Zvx=K€-,^ ] snoaua3ouoy Jeaui7 S! KzvxeK€-,4 "9 snoaua3owoyuou Jeaui7 S! Zvx= K€-,^ 'J23JJ0JU! SI suo/juasse Buimoiio} 34}J0 4pi4Mz uopsano'asuodsaj 5/Y1 aaES IlIm uopsanb Jayioue 01 Jumow
"asuodsaJ S/4 J^ES IIIM uopsanb Jayjoue 01 BuMOW !llnoujag S! A{xkva =Zvf {x}va+ ^ ajqexedas S! {Kz+xhva = Kx "P aiqejedas s! K + Zvx=K€-,^ ] snoaua3ouoy Jeaui7 S! KzvxeK€-,4 "9 snoaua3owoyuou Jeaui7 S! Zvx= K€-,^ 'J23JJ0JU! SI suo/juasse Buimoiio} 34}J0 4pi4M z...

-- 0.065824--