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A particle of mass m moves in a parabolic potential (energy): \(V(x) = \frac{1}{2} m\omega_{0}^{2}x^{2}\)
(a)(Griffiths Intro to QM, 2nd ed) finds the first excited state \(\psi_{1}(x)\)
Use the ladder operator a+ to find the second excited state wave function \(\psi_{2}(x)\)
(b) Demonstrate the orthogonality of the states \(\psi_{0}(x), \psi_{1}(x),and\psi_{2}(x)\) by direct integration.
A baseball is projected horizontally with an initial speed of 24.5 m/s from a height of 2.19 m. At what horizontal distance will the ball hit the ground
An object of mass 50.5 g is initially placed in boiling water so that it is at 101° C. Then the object is dropped into a calorimeter, Find the specific heat of the object
What was the bullet's speed as it left the barrel. A 1kg block rests against one end of a horizontal spring which is compressed by 10 $cm$.
Three equal 1.49 µC pointcharges are placed at the corners of an equilateral triangle whosesides are 0.500 m. What is the potential energy of the system? (Take zero as the potential energy of the three charges when they are infinitely far apart.)
A generator uses a coil that has 210 turns and a 0.20-T magnetic field. The frequency of this generator is 60.0 Hz, and its emf has an rms value of 120 V. assume that each turn of the coil is a square (an approximation), conclude the length of wire f..
The field has a magnitude of 0.5 T and is oriented in the +z direction. The particle is deflected in the -y direction and traces out of a fragment of a circle of radius 0.1m. what is the charge to mass ratio
An electron with an initial speed of 5.50×10^5m/s is brought to rest by an electric field. What was the potential difference that stopped the electron
A cup of water is heated with a heating coil that delivers 14.87W of heat. What is the mass of the water
Two capacitors, C1 = 2.0mF and C2 = 7.0mF , are in series, Find the charge stored on the second capacitor
A hollow non-conductiong sphere has a uniform charge density ?. The inner and outer radius of the sphere are r1 and r2m respectively. What is the total charge of this sphere
What is the tangential velocity of a satellite in a circular orbit 300km above the surface of the Earth, How long does the satellite take to complete one orbit
A microwave radio transmitter emits electromagnetic waves of a single wavelength. calculate the maximum magnetic field at this distance
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