Wo states | φ 1 ⟩ and | φ 2 ⟩ are stationary states with energy eigenvalues e1 and e2. their position-space representations are φ 1 ( x ) and φ 2 ( x ). let a state at time t = 0 be given by | ψ ( 0 ) ⟩ = 1 2 ( | φ 1 ⟩ + | φ 2 ⟩ ). write the position-space representation for | ψ ( t ) ⟩.

a_n = a_1 + (n - 1)d

the first term is 6.

the common difference d = ?

when you find d, replace n with 7 and d with the common difference to find your answer.

large crystals result from very slow cooling.

evaporation of water: this would produce an evaporite which is a sedimentary rock. like a salt pan in a desert. not possible to have volcanic rocks originate this way.

crystalization in molten earth: slow cooling over time. (hundreds to millions of years)

crystalization at earth's surface: this results in fast cooling. (a few hours to a few months or years)

crystalization from cooling off hot water: that would be a hydrothermal deposit. while associated with volcanics they are not volcanic rocks themselves and usually occur fairly rapidly.