 # Sriman Dutta

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## Everything posted by Sriman Dutta

1. Yes I know that the position wavefunction and momentum wavefunction are a Fourier pair. But their corresponding operators x^ and p^ (I'm representing the operators here) are non-commutative. So what's the connection between the two facts? PS: Forget just x and p. The uncertainty principle is valid for any pair of Fourier pair of variables a and b. and same it is true for any pair of non-commutative operators A and B. How's all this get in together?
2. Hi guys! Back after a lot of days ! :) So I was studying quantum mechanics and gor interested to find out the derivation of uncertainty principle. In the course of doing this, I found there were two kinds of derivations. One is relating the uncertainty principle as a basic fundamental property of Fourier transform and deriving it from Fourier transform. The other one uses operators and derives the relation by exploiting the non-commutavity of two operators. My question is since the two derivations yield the same result, there must be some deep subtle connection between the two, or, between Fourier transformation and non-commutative operators. Please do throw some light! Cheers!
3. Just back from Sikkim tour.....

4. Fill in the blanks: f__k s_x boo_s p_n_s Here's the answers: fork,six,boots,pants. How many of you got them correctly ??
5. x isn't a function of any variable. It's the position vector of the block from the mean position.
6. Hi, I'm back after a lot of days...... Just came back with a thought... Suppose there is a block of mass m that has compressed a light ideal spring having spring constant k. Now, if we write the equation of motion for this system, then ma=-kx or a=-kx/m It's evident that a is a function of x. So we can differentiate it wrt x to gt the jerk j. So, j=-kv/m. But v is variable and still differentiable. And continuing it, we have an endless chain. So is it infinitely differentiable??
7. Law of conservation of mass only applies to a closed system where there is no conversion of mass to energy. In case some energy comes into account, we have to consider energy and mass together, because E=mc^2.
8. Suppose it's like this: F <--- |eng|= |wg1|=|wg2|=|wg3|=|wg4|=|wg5| So this is the train (or wagons). Assuming that each wagon weighs m and the engine is of mass M, then net acceleration a = F/(M+5m) So force exerted by wg2 on wg3 is = 3ma
9. ## Why does light not bend when the incident ray is perpendicular to the surface of glass,and instead,will pass through it without bending

Snell's Law states that the ratio of the sine of the angle of incidence to the sine of angle of refraction is a constant for a given medium.
10. For the first question, total distance covered = length of train + length of bridge. For the second one, draw a displacement time graph.
11. Average speed is equal to total speed by total time. We can assume the total distance as d in the above question and proceed.
12. Such fantasies can be a part of a Hollywood movie. No idea, what would happen except explosion and wiping out of the life.
13. Photons are chargeless particles. Therefore they do not exert an electrostatic force of attraction on negatively-charged electrons, having o charge of -1.6 X 10^-19 coulomb.
14. Equations of Motion 1. $v=u+at$ 2. $S=ut+\frac{1}{2}at^2$ 3. $v^2 = u^2 +2aS$ Displacement during the nth second: $S_n = u+\frac{a}{2}(2n+1)$ For free fall in one-dimension; $h_{max} = \frac{u^2}{2g}$ time taken to reach highest point: $t_o = \frac{u}{g}$ When $t<t_o$ $distance = displacement = ut-\frac{1}{2}gt^2$ When $t=t_o$ $distance = displacement = h_{max}$ When $t>t_o$ $displacement = ut -\frac{1}{2}gt^2$ $distance = h_{max} + \frac{1}{2}g(t-t_o)^2$ Projectile Motion When $u$ is the initial velocity and $\theta$ is the launch angle given; $v_x = ucos\theta$ and $v_y=usin\theta -gt$ $a_x=0$ and $a_y =-g$ $x=utcos\theta$ and $y=ut sin \theta -\frac{1}{2}gt^2$ Time of flight: $T=\frac{2usin\theta}{g}$ Range : $R=\frac{u^2 sin 2\theta}{g}$ Maximum height : $h_{max} = \frac{u^2 sin^2 \theta}{2g}$ Equation of the path of projectile: $y = xtan \theta - \frac{gx^2}{2u^2cos^2 \theta }$ Relation between $R$ and $h_{max}$ is : $R=\frac{4h_{max}}{tan \theta}$
15. Lets start a thread that includes all important as well as useful concepts and equations commonly found in kinematics, mechanics, Newtonian physics and the whole classical physics in general. Lets see how far the list goes....... Newton's Laws of Motion 1. Every body continues its state of rest or uniform motion in a straight line until and unless it is acted upon by an external force. 2. The force impacted by a body is directly proportional to the rate of change of linear momentum. $F = \frac{dp}{dt}$ Or, $F=ma$ 3. Every action has an equal and opposite reaction. $F_1 = -F_2$
16. I'm presently studying in a high school. And I must agree that it's course is quite good, preparing you for advanced learning. Physics has got an amalgam of motion and kinematics and electromagnetism. Plenty of new concepts in chemistry have been introduced like the atomic structure in terms of orbitals, wave function, the uncertainty principle and Schrödinger equation as well. Also, it includes organic aromatic compounds and stoichiometry. In maths, calculus and trigonometry and 3d geometry and analytical mathematics have been introduced. I dare say, I will be half as smart as some of the members here after 12th.
17. How can we exclude mathematics from the field of science? The techniques of mathematics are also based on the nature of observable features. For instance, vectors have been designed to meet the requirements of motion and quantities posing a definite direction.
18. I obtained 95.6% in my 10th standard board examination. I'm really happy. 1. Show previous comments  4 more
2. No idea what IIT is - but congratulations on the excellent results - my Dad would have said "what happened to the other 4.4% percentage? Are you slipping?" But it would only be ever said in jest and followed by more hearty congratulations. So well done - be proud

3. Thanks for your congrats. IIT is the Indian Institute of Technology, the university from which the present CEO of Google, Sundar Pichai qualified. It's a chain of engineering colleges.

4. Congratulations.

19. Hello studiot, the functions that you gave can't be written in the algebraic forms. In other words, these functions give their outputs, but doesn't show how the process gives the result. So I suspect we can't try that here.
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