# Linear combination of separable solutions of Schrodinger's equation is not an energy eigen function

My doubt was that if a linear combination of separable solutions is also a solution of the Schrodinger's equation, but the linear combination doesn't necessarily satisfy the time independent part, it implies that the linear combination might not be an energy eigen function. This means that it will not have a definite value of energy, even though the wavefunctions out of which it is made of do have a definite value of energy.

Moreover, since the linear combination is also a separable solution of the Schrodinger's equation, it should have had a definite value of energy (as per Introduction to Quantum Mechanics by Griffiths). Where am I going wrong?

• A superposition of solutions with different eigenvalues ( = different values of the energy) does not have a well-defined energy. One can talk about the energy of the state in the sense of the expectation value of the Energy, will give a weighted average of the contributions of each component of the superposition. But the state is not an eigenstate of the Hamiltonian and does not a single energy value.
– user245141
Oct 27, 2019 at 8:47