I asked a physicist (former head of the physics department in a university) about some of the basics of quantum theory and the double slit experiment. Here is his reply. Are any of these points incorrect?
Electrons and light are always particles and never waves. There is no such thing as an electron wave. Ditto for light. However, electrons are quantum particles which behave very differently from classical particles.
In the two-slit experiment, the electron does not go through both slits at the same time. This can be confirmed experimentally by placing detectors at both slits and then sending an electron toward the slits. One finds that only one detector goes off. Both detectors never go off, confirming that the electron did not go through both slits.
A particle cannot be in two places at the same time.
The interference pattern for electrons (through a double slit) does not indicate that electrons are waves. Electrons are particles, but they are quantum particles, and quantum particles can produce an interference pattern.
The solution to the Schroedinger Equation is a probability amplitude, and not a wave function because there is no such thing as an electron wave.
Superposition does not mean that the particle is in, say, two energy states E1 and E2 at the same time. Superposition means that the particle has a non-zero probability (say 40%) to yield energy E1 and a non-zero probability (say 60%) to yield energy E2 upon performing a measurement. One obtains this result because quantum theory is a probabilistic theory of nature. It is impossible to know the energy of the particle before a measurement is performed. There is one exception to this rule, but I will not discuss it here.
edit: regarding what is a particle he replied: A particle is a localized entity that can pass through only one slit. A wave is an extended entity that can pass through both slits at the same time.