Yes, it is indeed possible for a quantum mechanical state to be in a superposition or non-orthogonal states. In fact, superposition is one of the fundamental concepts of quantum mechanics.
In quantum mechanics, the state of a system is described by a mathematical object called a wave function. The wave function represents the probabilities of different outcomes when a measurement is made on the system. A superposition occurs when a system is in a state that is a combination of multiple, distinct states. Mathematically, this is represented by adding together the wave functions corresponding to each state in the superposition.
For example, consider a spin-1/2 particle, such as an electron. The spin of the electron can be measured along different directions, let's say up or down along the z-axis. In the absence of measurement, the spin state can be in a superposition of both up and down states. This means the particle's wave function is a combination of the wave functions for spin-up and spin-down states.
Non-orthogonal states, on the other hand, refer to states that are not orthogonal or mutually exclusive to each other. Orthogonal states are states that have no overlap with each other and are completely distinct. In quantum mechanics, states can be orthogonal or non-orthogonal. Superposition and non-orthogonality are not mutually exclusive concepts. A superposition can involve both orthogonal and non-orthogonal states.
To summarize, quantum mechanics allows for the existence of superposition states where a system can be in a combination of different states, and these states can be either orthogonal or non-orthogonal to each other.