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A beam of mono-energetic particles having speed v is described by the wave function $$\psi $$ (x) = u(x) exp(ikx), where u(x) is a real function. This corresponds to a current density

A beam of mono-energetic particles having speed v is described by the wave function $$\psi $$ (x) = u(x) exp(ikx), where u(x) is a real function. This corresponds to a current density Correct Answer u<sup>2</sup>(x)v

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A particle of mass m is confined in the potential
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\[V\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{2}m{\omega ^2}{x^2},}&{{\text{for }}x Let the wave function of the particle be given by $$\psi \left( x \right) = - \frac{1}{{\sqrt 5 }}{\psi _0} + \frac{2}{{\sqrt 5 }}{\psi _1}$$
where $${\psi _0}$$ and $${\psi _1}$$ are the eigen functions of the ground state and the first excited slate respectively. The expectation value of the energy is
Consider the following statements with regards to the shear force diagram for the beam ABCD: 1. The beam ABCD is an overhanging beam having supports at A and D only. 2. The beam carries a point load of 20 kN at C. 3. The beam carries a concentrated load of 10 kN at the end B. 4. The beam is an overhanging beam having supports at C and D only. 5. The beam carries a uniformly distributed load of 70 kN over the left hand portion AC only. Which of the above statements are correct?
What is the distance covered by boat N upstream in 5 hours? Which of the following option is sufficient alone to find the answer? A) Boat M is travelling downstream with 20% more downstream speed of boat N. Speed of boat M in still water is 10% more than the speed of boat N in still water. B) Boat M and Boat N are travelling downstream with speed 33 km/hr and 40 km/hr respectively and speed of boat M is still water is 2 times the speed of stream. C) Speed of boat M in still water is 6 km/hr less then speed of boat N in still water and speed of stream is 10 km/hr. D) Speed of stream is ½ times the speed of boat N in still water and downstream speed of boat M is 44 km/hr. E) Speed of stream is 10 km/hr and ratio of upstream speed of boat M and boat N is 3 : 2 respectively.
Consider the following statements regarding types of supports and beams: 1. When both supports of beams are roller supports, the beam is known as simply supported beam. 2. A beam with one end fixed and the other end free is known as fixed beam. 3. A beam with both ends fixed is known as cantilever beam. 4. A beam with one end fixed and the other simply supported is known as propped cantilever. Which of the above statements is/are correct ?
An object X sinks in liquids P and Q but floats in liquid R. Which of the following conclusions can be made from these observations? A) Density of X is more than the density of P B) Density of X is less than the density of R C) Density of P is equal to the density of R D) Density of P is less than the density of R
Seven people A, B, C, D, E, F and G live on separate floors of a 7-floor building. Ground floor is numbered 1, first floor is numbered. 2 and so on until the topmost floor is numbered 7. Each one of these having a different cars-Cadillac, Ambassador, Fiat, Maruti, Mercedes, Bedford and Fargo but not necessarily in the same order. Only three people live above the floor on which A lives. Only one person lives between A and the one having a car Cadillac. F lives immediately below the one having a car Bedford. The one having a car Bedford lives on an even-numbered floor. Only three people live between the ones having a car Cadillac and Maruti. E lives immediately above C. E is not having a car Maruti. Only two people live between B and the one having a car Fargo. The one having a car Fargo lives below the floor on which B lives. The one having a car Fiat does not live immediately above D or immediately below B. D does not live immediately above or immediately below A. G does not have a car Ambassador. Question : How many people live between the floors on which D and the one having a car Bedford ?
In which of the following cases, there exists the situation of Pure Bending in some part of the beam or along the entire beam? i) A simply supported beam subjected to two equally spaced downward concentrated loads ii) A simply supported beam subjected to two equally spaced opposite moments iii) A cantilever beam subjected to clockwise moment at free end iv) An overhanging beam with both side overhangs subjected to different concentrated loads at both the free ends
According to morphological details, pSi can be divided as sponge-like pSi and pSi featuring cylindrical pores.
\(\psi\)MO = \(\psi\)A + \(\psi\)B.
If $${\text{sin}}\left( {{{60}^ \circ } - \theta } \right)$$   = $${\text{cos}}\left( {\psi - {{30}^ \circ }} \right),$$   then the value of $${\text{tan}}\left( {\psi - \theta } \right)$$   is (assume that $$\theta $$ and $$\psi $$ are both positive acute angles with$$\theta {30^ \circ }$$  ) ?