Question:

Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de Broglie wavelengths are λ₁ and λ₂, their de Broglie wavelength in the frame of reference attached to their centre of mass is:

λCM = λ₁ = λ₂

1/λCM = 1/λ₁ + 1/λ₂

λCM = 2λ₁λ₂√λ₁² + λ₂²

λCM = (λ₁ + λ₂)/2

Since λ = h/mv, v = h/mλ
Let v₁ and v₂ are the speeds of electrons
vcm = (v₁ + v₂)/2
h²/mλcm = ½(h/mλ₁ + h/mλ₂)
1/λcm = 1/λ₁ + 1/λ₂