List of top Quantum Mechanics Questions

Consider a state described by \[ \psi(x, t) = \psi_2(x, t) + \psi_4(x, t), \] where} \( \psi_2(x, t) \) and \( \psi_4(x, t) \) are respectively the second and fourth normalized harmonic oscillator wave functions and \( \omega \) is the angular frequency of the harmonic oscillator. The wave function \( \psi(x, t = 0) \) will be orthogonal to \( \psi(x, t) \) at time \( t \) equal to
 

A matter wave is represented by the wave function \[ \Psi(x, y, z, t) = A e^{i(4x+3y+5z-10\pi t)}, \] where A is a constant. The unit vector representing the direction of propagation of this matter wave is
 

Three non-interacting bosonic particles of mass \( m \) each, are in a one-dimensional infinite potential well of width \( a \). The energy of the third excited state of the system is \( x \times \frac{h^2 \pi^2}{ma^2} \). The value of \( x \) (in integer) is \(\underline{\hspace{2cm}}\).