Aparticle of mass m in a 1d harmonic oscillator with frequency w, at time t = 0 is in a linear superposition of the ground and the first excited eigenstates, specifically, it has wave function 14(x,0)) - a[14) +expliq) 4.)]. (a) normalize the wave function. (b) find the coefficients cn in the series expansion 144(x,1)) - cm14(x)) exp[-i e,1/ħ]. if the energy is measured at time t, what are the possible values and what are the probabilities? find the expectation value of the hamiltonian ((x, t)|h1 4(x, t)) in this state. (c) find the expectation value of the momentum of the particle at time t, (4(x, t) p14(x, (d) find the value of the phase q such that (p) reaches its maximum value at time t=0. hint: you can take derivatives, or you can use eq. 2.69: =iħmo/2câ. - â

the answer is b, have negligible mass

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.

according to jean piaget, in what stage of cognitive development are children able to understand conservation task?

b. preoperational

just took it