Thus there is no uncertainty in superposition principle. I can prepare system with only up spin atoms by doing a SG experiment. It is like assigning amplitudes to different normal modes depending on where the string was plucked. These probabilities depend on the way the system was prepared. Thus the general state of the system is a superposition of all the possible states weighted by certain probability. However there is a certain probability associated with each feasible state. But experimental observations of quantum systems show that a system can remain in any of the many states those satisfy the Schrödinger equation.

Principle of superposition: Classical mechanics says that a particle can stay in a particular state in a particular instant of time. Thus uncertainty principle negates the classical determinacy by saying that you 'can not measure' the position and momentum of a system simultaneously then how can you specify them as demanded by determinacy idea? So the uncertainty principle is a purely non classical principle. Classical mechanics says that 'if one knows the positions and momenta of particles of a system then one can predict the future states of the system by using Newton's laws'. Uncertainty principle: It says that it is impossible to measure conjugate measurables such as position and momentum simultaneously. Uncertainty principle is not the cause of Superposition principle and vice versa. But our discussion will remain concentrated for the wave having equal or nearly equal frequencies.I think 'the principle of superposition' and 'the uncertainty principle' are two different and distinct principles used in quantum mechanics.

Whatever may be the frequencies or direction of the waves this law is always applicable for their superposition. (iii) The principle of superposition is a general law. But in case of the light wave or any other electro-magnetic waves, this law is not properly applied. travel through inertia media and if in those cases the amplitude of the superposed waves is less only then this law is applicable. (ii) When water waves (ripples), sound waves etc. When taking photographs light waves coming from different objects when entering through the shutter of a camera, they do not interfere with each other: consequently, we get the distinct picture of each object. When two or three persons talk at a time we understand their voice clearly and unchanged. If two stones are thrown on the water surface, two circular waves that are generated can travel through each other with equal and unchanged speed, shape and velocity. (i) From our everyday experience, we can realize that different waves travelling through a particular medium can travel independently. Observe the following applications of superposition principle: If the two displacements travel along a straight line in the same direction, then “+ ve” sign is used and if these wave move in opposite direction along the straight line, then “- ve” sign is to be used. If the displacement of a particle for the first wave is y 1 and displacement at that particle is y 2, then according to this law, the resultant displacement will be, Suppose, two waves are travelling simultaneously through a medium. This principle is known as the principle of superposition of wave.

Law: – When two or more waves pass simultaneously through the same medium, the resultant displacement of each particle of the medium at any instant is equal to the vector sum of the displacements produced by the waves separately.

Principle of superposition in mechanics