# What is the equation of motion for a system which is given below:

1. The Lagrangian for a mechanical system is L = cq̇2 + dq4
2. where c and d are constants
3. q is a generalized coordinate
1. q̈ = 2d/c * q3
2. q̈ = -2d/c * q3
3. q̇ = d/c * q3
4. q̇ = √d/c * q2

# Find the expectation value of the position of a particle:

1. The wave function of a particle is  Ψ = ax
2. and a  particle is limited to the x-axis between x = 0 and x = 1
3. the wave function of a particle is Ψ = 0 elsewhere
4. find the expectation value <x̂> of the position particle.
1. Zero
2. a/2
3. a2/4
4. a2

# The energy of a simple harmonic oscillator can be described quantum-mechanically as:

1. En = (n + 1/2)ℏω
2. En = (n + 3/2)ℏω
3. En = (n + 1/2)ω
4. All of the  above

# The eigenvalues of Hermitian operators are:

1. Imaginary
2. Complex number
3. Real
4. None of the above

# The sum of two Hermitian operators is:

1. Hermitian
2. Anti-Hermitian
3. Commutator
4. None of these

# The quantity 〈Φ | ψ〉 represent:

1. Probability amplitude
2. Orthonormality
3. Orthogonality
4. None of the above